Pay growth and prices picked up, keeping the Fed on track for rate increases.

Wages, prices and consumer spending all continued to climb, the latest government data showed Friday — fresh evidence that the economy remains resilient amid fear of a recession, but also that inflation is likely to remain a vexing problem for the Federal Reserve.

Consumer prices climbed 6.8 percent over the year through June, according to the Fed’s preferred inflation gauge, the Personal Consumption Expenditures measure. That was the fastest pace since 1982. Consumer spending rose even faster than prices, though, as Americans shelled out money for cars, vacations and restaurant meals even as higher gas and grocery bills strained household budgets.

Meanwhile, paychecks grew briskly, albeit not enough to keep up with inflation. The Employment Cost Index for the second quarter rose 5.1 percent from a year earlier.

Taken together, the data released Friday indicated that the consumer economy has retained momentum in the face of the highest inflation in decades. That should ease concerns that an economic downturn has already begun but, paradoxically, could also make future economic pain more likely: Strong demand will put continued upward pressure on prices, potentially forcing the Fed to react more aggressively to cool demand and bring inflation under control.

Central bank officials on Wednesday made their second supersize rate increase in a row — three-quarters of a percentage point — as they try to slow down the economy by making money more expensive to borrow. They have signaled that they will closely watch incoming economic readings as they consider whether to make another giant move at their next meeting in September, and a number of economists said Friday’s data were likely to prod the officials toward continued decisive action.

“This is a print that’s going to keep Fed officials up at night,” Omair Sharif, founder of Inflation Insights, wrote in reaction to the fresh wage data. “The monthly inflation and activity data are going to have to cooperate in a very big way for the Fed to step down.”

Jerome H. Powell, the Fed chair, said during his news conference this week that officials could raise interest rates three-quarters of a point again, though he did not commit to such a move. The Fed has nearly two months, and a lot of economic data to parse, between now and its next rate decision.

Neel Kashkari, president of the Federal Reserve Bank of Minneapolis, said in an interview on Friday that raising rates half a point at upcoming meetings “seems reasonable” to him. But he noted that inflation data had been surprising “in a bad way” and said that if core inflation remained high, it could push him to think a three-quarter point move was needed.

“It continues to be concerning,” Mr. Kashkari said of the data released Friday. “I’m waiting for some good news to come: Some surprises that, oh, inflation was lower than we were expecting.”

As rapid price increases challenge the Fed, they are also dogging the White House, which called Friday’s inflation numbers “too high.”

“The president will continue to do everything in his power to tackle inflation and work with Congress to lower prices,” Cecilia Rouse, chair of President Biden’s Council of Economic Advisers, said in a statement after the release.

Gas prices have dropped sharply this month, which should pave the way for slower inflation in July data. But it is not clear how durable those changes will be, and there are plenty of other worrying signs about the inflation outlook.

Prices have been increasing rapidly for more than a year, and central bankers are focused on trying to restrain demand and drive inflation lower before it becomes ingrained. Once consumers and businesses begin to expect and accept ever-higher costs, it may be harder to quash them: Workers could begin to ask for higher wages to cover their higher costs, and companies may begin steadily raising prices to cover their climbing labor bills in an upward spiral.

Most economists think that America is not there yet, but wage growth has picked up — probably to a point that would make it difficult for price increases to moderate back toward the Fed’s 2 percent inflation target. Companies are unlikely to stop raising prices when their labor bills are increasing so much.

That is why Friday’s Employment Cost Index data are problematic for the Fed. The report’s wages and salaries measure rose 5.3 percent from a year earlier before being adjusted for inflation, up notably from 4.7 percent in the previous reading. Private wages and salaries climbed an even more robust 5.7 percent.

While there was some moderation in benefits pay — and a measure of wages and benefits for workers who do not receive incentive pay eased slightly — the report as a whole suggested that employers were paying up as they tried to retain workers and lure new ones in a labor market with plentiful job openings.

And the details of the inflation report made clear that price pressures remained strong. A core inflation measure, which strips out volatile food and fuel prices to get a sense of underlying inflation trends, had been slowing down on a monthly basis. That reversed in June: Prices climbed 0.6 percent from the previous month, the fastest reading in more than a year and up from 0.3 percent in May.

After more than a year of waiting in vain for inflation to peak, economists are looking toward consumer spending for a signal of when, and how much, it might finally moderate.

Analysts have been predicting for months that consumers will eventually find themselves unable to keep up with climbing costs, which will prompt them to slow their spending so much that it weighs on demand and allows supply to catch up.

May’s spending report had suggested that the pullback might be beginning, but buyers staged a comeback in June. Spending overall rose 1.1 percent, slightly faster than the 1 percent monthly increase in consumer prices.

“Airplanes and trains are overbooked, hotels are near capacity, and leisure groups are reporting very strong demand indicating a willingness to spend over the summer,” Greg Daco, chief economist at EY-Parthenon, wrote after the release.

Strong demand for cars, exercise equipment and physical goods has helped push prices up over the past year. Policymakers have been hoping that, as the pandemic eases, consumers will shift back to spending on services, allowing supply chains to catch up and inflation to cool.

Yet that transition has happened only slowly. Spending on services rose in June, but so did spending on goods, even adjusted for inflation. Spending on cars and car parts rose 2.5 percent in June after falling in May.

“We had this narrative going into the year that consumption would shift from goods to services, but consumers continued to spend” on goods, said Blerina Uruci, an economist at T. Rowe Price.

Still, incomes rose more slowly than prices in June, and consumers compensated by saving at the lowest rate since 2009 — a trend that won’t be sustainable in the long run. And there are other reasons to think that both price growth and spending may soon crack.

Airfares have been declining this month, economists said, which should take some pressure off inflation in July, and the broader economy shows some signs of cooling. Used cars, which have been in short supply for more than a year and a big factor in inflation, are finally returning to some car sales lots as demand for pre-owned vehicles wanes.

“In our bifurcated economy, used-vehicle buyers are more likely to be more negatively impacted by higher prices for energy, food and rent,” Jonathan Smoke, chief economist at Cox Automotive, wrote in a research note this week.

Large retailersincluding Walmart have noted that consumers are buying fewer goods as they pay more for food and find their budgets strained.

And some data points suggest that the economy is already in trouble. The economy sank for the second quarter in a row after inflation is taken into account, data released Thursday showed, which is a common though unofficial definition of a recession.

But those signals are far from conclusive. That G.D.P. data will be revised, and many economists cautioned against reading too much into it when job growth remains robust.

As they parse conflicting economic signals, investors are carefully eyeing the Fed, trying to guess how much it might raise interest rates at its Sept. 20-21 meeting and what it makes of any slowdown.

“I don’t think the country is in a recession, but on some level that’s not the right question: I think the right question is whether current economic conditions are creating hardship,” Raphael Bostic, the president of the Federal Reserve Bank of Atlanta, said in an NPR interview published Friday morning. “There are a lot of people hurting, and because of that, we really need to address the high levels of inflation.”