PARIS — The European Central Bank’s top task is to keep inflation at bay. But as the cost of everything from gas to food has soared to record highs, the bank’s employees are joining workers across Europe in demanding something rarely seen in recent years: a hefty wage increase.

“It seems like a paradox, but the E.C.B. isn’t protecting its own staff against inflation,” said Carlos Bowles, an economist at the central bank and vice president of IPSO, an employee trade union. Workers are pressing for a raise of at least 5 percent to keep up with a historic inflationary surge set off by the end of pandemic lockdowns. The bank says it won’t budge from a planned a 1.3 percent increase.

That simply won’t offset inflation’s pain, said Mr. Bowles, whose union represents 20 percent of the bank’s employees. “Workers shouldn’t have to take a hit when prices rise so much,” he said.

Inflation, relatively quiet for nearly a decade in Europe, has suddenly flared in labor contract talks as a run-up in prices that started in spring courses through the economy and everyday life.

From Spain to Sweden, workers and organized labor are increasingly demanding wages that keep up with inflation, which last month reached 4.90 percent, a record high for the eurozone.

Austrian metalworkers wrested a 3.6 percent pay raise for 2022. Irish employers said they expect to have to lift wages by at least 3 percent next year. Workers at Tesco supermarkets in Britain won a 5.5 percent raise after threatening to strike around Christmas. And in Germany, where the European Central Bank has its headquarters, the new government raised the minimum wage by a whopping 25 percent, to 12 euros (about $13.60) an hour.

The upturns follow a bout of anemic wage growth in Europe. Hourly wages fell for the first time in 10 years in the second quarter from the same period a year earlier, although economists say pandemic shutdowns and job furloughs make it hard to paint an accurate picture. In the decade before the pandemic, when inflation was low, wages in the euro area grew by an average of 1.9 percent a year, according to Eurostat.

The increases are likely to be debated this week at meetings of the European Central Bank and the Bank of England. E.C.B. policymakers have insisted for months that the spike in inflation is temporary, touched off by the reopening of the global economy, labor shortages in some industries and supply-chain bottlenecks that can’t last forever. Energy prices, which jumped in November a staggering 27.4 percent from a year ago, are also expected to cool.

The E.C.B., which aims to keep annual inflation at 2 percent, has refrained from raising interest rates to slow climbing prices, arguing that by the time such a policy takes effect, inflation would have eased anyway on its own.

“We expect that this rise in inflation will not last,” Christine Lagarde, the E.C.B. president, said in an interview in November with the German daily F.A.Z., adding that it was likely to start fading as soon as January.

In the United States, where the government on Friday reported that inflation jumped 6.8 percent in the year through November, the fastest pace in nearly 40 years, officials are not so sure. In congressional testimony last week, the Federal Reserve chair, Jerome H. Powell, stopped using the word “transitory” to describe how long high inflation would last. The Omicron variant of the coronavirus could worsen supply bottlenecks and push up inflation, he said.

In Europe, unions are also agitated after numerous companies reported bumper profits and dividends despite the pandemic. Companies listed on France’s CAC 40 stock index saw margins jump by an average of 35 percent in the first quarter of 2021, and half reported profits around 40 percent higher than the same period a year earlier.

Workers say that they have not benefited from such gains, and that inflation has made things worse by abruptly slashing their purchasing power. Companies, for their part, are wary of linking salaries to inflation — a policy that also makes the European Central Bank nervous.

Surging energy costs have been “a shock on incomes,” said James Watson, chief economist for Business Europe, the largest business trade association. “But if you try to compensate by raising wages, there’s a risk that it’s unsustainable and that we enter into a wage-price spiral,” he said.

European policymakers are watching carefully for any signs that companies are passing the cost of higher wages on to consumers. If that happens, it could create a dangerous run-up of higher prices that might make inflation chronic.

For now, that seems unlikely, in part because wage negotiations so far haven’t resulted in outsize pay increases, said Holger Schmieding, chief economist at Berenberg Bank in London.

Negotiated wage increases have been averaging around 2.5 percent, below inflation’s current pace. “Will wage hikes be inflationary? Not really,” he said. “The eurozone is not at a severe risk.”

But as climbing prices continue to unnerve consumers, labor organizations are unlikely to ease up. Gasoline prices recently hit €2 a liter in parts of Europe — equal to over $8 a gallon. Higher transportation costs and supply chain bottlenecks are also making supermarket basics more expensive.

Justine Negoce, a cashier at France’s largest home-improvement chain, joined an unprecedented companywide walkout in Paris last month to demand a hefty raise as rising prices gobbled up her modest paycheck.

After employees blocked warehouses for 10 days and demonstrated in the cold, the company, Leroy Merlin, agreed to a 4 percent raise for its 23,000 workers in France — twice the amount that management originally offered. The company, owned by Adeo, Europe’s biggest DIY chain, saw revenue climb over 5 percent in 2020 to €8 billion as housebound consumers decorated their homes and people like Ms. Negoce worked the front lines to ring up sales.

Her monthly take-home pay will rise in January to €1,300 from €1,250. The additional cash will help offset a 25 percent jump in grocery and gas bills for her two teenage children and husband — just barely.

On a recent trip to the supermarket, her basket of food basics, including rice, coffee, sugar and pasta, jumped to €103 instead of the €70 to €80 she paid a few months back. Filling her gas tank now costs €75 instead of €60. And even with her husband’s modest salary, she said, the couple will still be in the red at the end of the month.

“We’re happy with the raise, because every little bit helps,” Ms. Negoce said. “But things are still tight, and we’ll need to count every penny.”

In a statement, Leroy Merlin said the agreement maintains employees’ purchasing power and puts its average salaries for next year at 15 percent above France’s gross monthly minimum wage, which the government raised in October by 2.2 percent.

Crucially, executives also agreed to return to the bargaining table in April if a continued upward climb in prices hurts employees.

At Sephora, the luxury cosmetics chain owned by LVMH Moët Hennessy Louis Vuitton, some unions are seeking an approximately 10 percent pay increase of €180 a month to make up for what they say is stagnant or low pay for employees in France, many of whom earn minimum wage or a couple hundred euros a month more.

LVMH, which recorded revenue of €44.2 billion in the first nine months of 2021, up 11 percent from 2019, raised wages at Sephora by 0.5 percent this year and granted occasional work bonuses, said Jenny Urbina, a representative of the Confédération Générale du Travail, the union negotiating with the company.

Sephora has offered a €30 monthly increase for minimum wage workers, and was not replacing many people who quit, straining the remaining employees, she said.

“When we work for a wealthy group like LVMH no one should be earning so little,” said Ms. Urbina, who said she was hired at the minimum wage 18 years ago and now earns €1,819 a month before taxes. “Employees can’t live off of one-time bonuses,” she added. “We want a salary increase to make up for low pay.”

Sephora said in a statement that workers demanding higher wages were in a minority, and that “the question of the purchasing power of our employees has always been at the heart” of the company’s concerns.

At the European Central Bank, employees’ own worries about purchasing power have lingered despite the bank’s forecast that inflation will fade away.

A spokeswoman for the central bank said the 1.3 percent wage increase planned for 2022 is a calculation based on salaries paid at national central banks, and would not change.

But with inflation in Germany at 6 percent, the Frankfurt-based bank’s workers will take a big hit, Mr. Bowles said.

“It’s not in the mentality of E.C.B. staff to go on strike,” he said. “But even if you have a good salary, you don’t want to see it cut by 4 percent.”

Léontine Gallois contributed reporting from Paris.

A few weeks ago, Representative Dan Crenshaw, a Texas Republican, falsely claimed that the centerpiece of President Biden’s domestic agenda, a $1.75 trillion bill to battle climate change and extend the nation’s social safety net, would include Medicare for all.

It doesn’t, and never has. But few noticed Mr. Crenshaw’s lie because he didn’t say it on Facebook, or on Fox News. Instead, he sent the false message directly to the inboxes of his constituents and supporters in a fund-raising email.

Lawmakers’ statements on social media and cable news are now routinely fact-checked and scrutinized. But email — one of the most powerful communication tools available to politicians, reaching up to hundreds of thousands of people — teems with unfounded claims and largely escapes notice.

The New York Times signed up in August for the campaign lists of the 390 senators and representatives running for re-election in 2022 whose websites offered that option, and read more than 2,500 emails from those campaigns to track how widely false and misleading statements were being used to help fill political coffers.

Both parties delivered heaps of hyperbole in their emails. One Republican, for instance, declared that Democrats wanted to establish a “one-party socialist state,” while a Democrat suggested that the party’s Jan. 6 inquiry was at imminent risk because the G.O.P. “could force the whole investigation to end early.”

But Republicans included misinformation far more often: in about 15 percent of their messages, compared with about 2 percent for Democrats. In addition, multiple Republicans often spread the same unfounded claims, whereas Democrats rarely repeated one another’s.

At least eight Republican lawmakers sent fund-raising emails containing a brazen distortion of a potential settlement with migrants separated from their families during the Trump administration. One of them, Senator John Kennedy, Republican of Louisiana, falsely claimed that President Biden was “giving every illegal immigrant that comes into our country $450,000.”

Those claims were grounded in news that the Justice Department was negotiating payments to settle lawsuits filed on behalf of immigrant families whom the Trump administration had separated, some of whom have not been reunited. But the payments, which are not final and could end up being smaller, would be limited to that small fraction of migrants.

The relatively small number of false statements from Democrats were mostly about abortion. For instance, an email from Representative Carolyn Maloney of New York said the Mississippi law before the Supreme Court was “nearly identical to the one in Texas, banning abortions after 6 weeks,” but Mississippi’s law bans abortion after 15 weeks and does not include the vigilante enforcement mechanism that is a defining characteristic of Texas’ law.

A spokeswoman for Ms. Maloney called the inaccuracy an “honest mistake” and said the campaign would check future emails more carefully.

Campaign representatives for Mr. Kennedy and Mr. Crenshaw did not respond to multiple requests for comment. The Republican House and Senate campaign committees also did not respond to a request for comment.

Politicians have exaggerated and dissembled since time immemorial, including in their email dispatches. But the volume, the baldness and the reach of the false claims have increased.

The emails reviewed by The Times illuminate how ubiquitous misinformation has become among Republicans, fueled in large part by former President Donald J. Trump. And the misinformation is not coming only, or even primarily, from the handful who get national attention for it.

The people behind campaign emails have “realized the more extreme the claim, the better the response,” said Frank Luntz, a Republican pollster. “The more that it elicits red-hot anger, the more likely people donate. And it just contributes to the perversion of our democratic process. It contributes to the incivility and indecency of political behavior.”

The messages also underscore how, for all the efforts to compel platforms like Facebook and Twitter to address falsehoods, many of the same claims are flowing through other powerful channels with little notice.

For fact checkers and other watchdogs, “it’s hard to know what it is that politicians are saying directly to individual supporters in their inboxes,” said Jennifer Stromer-Galley, a professor in the School of Information Studies at Syracuse University.

“And politicians know that,” she said. “Politicians and the consulting firms behind them, they know that this kind of messaging is not monitored to the same extent, so they can be more carefree with what they’re saying.”

Email is a crucial tool in political fund-raising because it costs campaigns almost nothing and can be extremely effective: When campaigns invest in it, it routinely accounts for a majority of their online fund-raising. Supporters are bombarded — sometimes daily — with messages meant to make them angry, because strategists know anger motivates voters.

In many cases, candidates used anger-inducing misinformation directly in their requests for a donation. For instance, after his false claim about payments to immigrants, Mr. Kennedy — who began the email by declaring himself “mad as a murder hornet” — included a link labeled “RUSH $500 TO STOP ILLEGAL PAYMENTS!”

“I’m watching Joe Biden pay illegals to come into our country, and it’s all being paid for by raising YOUR taxes,” he wrote. “We can’t let Biden pass out hundreds of thousands of dollars to every Tom, Dick and Harry that wants to come into our country illegally.”

Several other Republicans, including Representative Vern Buchanan of Florida, also claimed that the payments would go to all undocumented immigrants. Others, including Senator Todd Young of Indiana, tucked the context inside emails with misleading subject lines such as “BREAKING: Biden wants to pay illegal immigrants $450,000 each for breaking our laws.”

Of 28 emails that included the $450,000 figure, only eight contextualized it accurately.

Campaign representatives for Mr. Buchanan and Mr. Young did not respond to requests for comment.

Another common line was that the Justice Department was targeting parents as “domestic terrorists” for challenging the teaching of critical race theory, an advanced academic framework that conservatives are using as shorthand for how some curriculums cover race and racism — or, alternatively, for challenging pandemic-related restrictions.

“Parents are simply protesting a radical curriculum in public schools, and Biden wants the parents labeled terrorists,” read an email from Representative Jake LaTurner of Kansas. “Will you consider donating now to help us fight back against this disgusting abuse of power?”

This misinformation — echoed in emails from Mr. Crenshaw, Mr. Kennedy, Mr. Young, Representative Jim Hagedorn of Minnesota and Representative Elise Stefanik of New York — emerged after Attorney General Merrick Garland sent a memorandum on Oct. 4 directing the F.B.I. to address threats against school personnel and school board members. (Some opponents of curriculums and pandemic protocols have sent death threats, vandalized homes and otherwise acted menacingly.) The memo explicitly distinguished between dissent and threats, and did not call anyone a domestic terrorist. The Republican narrative conflates it with a letter the National School Boards Association, an independent group, sent to the Justice Department a few days earlier.

Representatives for Ms. Stefanik and Mr. Hagedorn said the association had “coordinated” with the Biden administration on the letter, citing recent news reports. Those reports say the school boards association discussed the letter with the administration and, at the administration’s request, added details about the threats; they do not show the Justice Department endorsing the “terrorist” label or criminalizing nonviolent opposition to curriculums.

Campaign representatives for Mr. Crenshaw, Mr. Kennedy, Mr. LaTurner and Mr. Young did not respond to requests for comment.

Combating misinformation in emails is difficult both because of the private nature of the medium and because its targets are predisposed to believe it — though Emily Thorson, a political scientist at Syracuse, noted that the fact that the recipients were likely to already be staunch partisans reduced the chances of misinformation reaching people whose views would be changed by it.

Professor Thorson said what concerned her more was that — unlike much of the misinformation on social media — these claims came from people with authority and were being spread repetitively. That is how lies that the 2020 election was rigged gained traction: not “because of random videos on Facebook but because it was a coherent message echoed by a lot of elites,” she said. “Those are the ones that we need to be most worried about.”

Mr. Luntz, the Republican pollster, runs frequent focus groups with voters and said they tended to accept misinformation uncritically.

“It may be a fund-raising pitch, but very often people look at it as a campaign pitch,” he said. “They think of it as context, they think of it as information — they don’t necessarily see this as fund-raising, even though that’s what it is. And so misleading them in an attempt to divide them from their money is pure evil, because you’re taking advantage of people who just don’t know the difference.”