A surprisingly robust June employment report reinforced that America’s labor market remains historically strong even as recession warnings reach a fever pitch. But that development, while good news for the Biden administration, is likely to keep the Federal Reserve on its aggressive path of interest rate increases as it tries to cool the economy and slow inflation.

Today’s world of rapid price increases is a complicated one for economic policymakers, who are worried that an overheating job market could exacerbate persistent inflation. Instead of viewing roaring demand for labor as an unmitigated good, they are hoping to engineer a gradual and controlled slowdown in hiring and wage growth, both of which remain unusually strong.

Friday’s report offered early signs that the desired cooling is taking hold as both job gains and pay increases moderated slightly. But hiring and earnings remained solid enough to reinforce the view among Fed officials that the labor market, like much of the economy, is out of whack: Employers still want far more workers than are available.

The new data will likely keep central bankers on track to make another supersize rate increase at their meeting later this month as they try to restrain consumer and business spending and force the economy back into balance.

“We’re starting to see those first signs of slowdown, which is what we need,” Raphael Bostic, president of the Federal Reserve Bank of Atlanta, said in a CNBC interview after the report was released. Still, he called the wage data “only slightly” reassuring and said that “we’re starting to inch in the right direction, but there’s still a lot more to do, and a lot more we’ll have to see.”

Fed officials began to raise interest rates from nearly zero in March in an attempt to make borrowing of many kinds more expensive. Last month, the central bank lifted its policy rate by 0.75 percentage points, the largest single increase since 1994.

Central bankers typically adjust their policy only in quarter-point increments, but they have been picking up the pace as inflation proves disturbingly rapid and stubborn. While Fed policymakers have said they will debate a move between 0.5 or 0.75 percentage points at their meeting on July 26 and 27, a chorus of officials have in recent days said they would support a second 0.75 percentage point move given the speed of inflation and strength of the job market.

As the Fed tries to tap the brakes on the economy, Wall Street economists have warned that it may instead slam it into a recession — and the Biden administration has been fending off declarations that one is already arriving. A slump in overall growth data, a pullback in the housing market and a slowdown in factory orders have been fueling concern that America is on the brink of a downturn.

The employment data powerfully contradicted that narrative, because a shrinking economy typically does not add jobs, let alone at the current brisk pace.

Mr. Biden celebrated the report on Friday, saying that “our critics said the economy was too weak” but that “we still added more jobs in the past three months than any administration in nearly 40 years.”

Private sector voices concurred that the employment report showed an economy that did not appear to be tanking.

“Wage growth remains elevated and rates of job loss are low,” Nick Bunker, economic research director at the job website Indeed, wrote in a reaction note. “We’ll see another recession some day, but today is not that day.”

The contradictory moment in the economy — with prices rising fast, economic growth contracting and the unemployment rate hovering near a 50-year low — has posed a challenge for Mr. Biden, who has struggled to convey sympathy for consumers struggling with higher prices while seeking credit for the strength of the jobs recovery.

Mr. Biden’s approval ratings have slumped as price growth has accelerated. Confidence has taken an especially pronounced battering in recent months amid rising gas prices, which topped $5 a gallon on average earlier this summer.

On Friday, Mr. Biden emphasized that fighting inflation was his top economic priority while also praising recent job market progress.

“I know times are tough,” Mr. Biden said, speaking in public remarks. “Prices are too high. Families are facing a cost-of-living crunch. But today’s economic news confirms the fact that my economic plan is moving this country in a better direction.”

But unfortunately for the administration and for workers across America, tackling high prices will probably come at some cost to the labor market.

As price increases bedevil consumers at the gas pump and in the grocery aisle, the Fed believes that it needs to bring inflation under control swiftly in order to set the economy on a path toward healthy and sustainable growth.

The Fed’s tool to achieve that positive long-term outcome works by causing short-term economic pain. By making money expensive to borrow, the central bank can slow down home buying and business expansions, which will in turn slow hiring and wage increases. As companies and families have fewer dollars to spend, the theory goes, demand will come into better alignment with supply and prices will stop rocketing higher.

Officials expect unemployment to eventually tick up as rate increases bite and the economy weakens, though they are hoping that it will only rise slightly.

Fed policymakers are still hoping to engineer what they often call a “soft landing,” in which hiring and pay gains slow gradually, but without plunging the economy into a painful recession.

But pulling it off will not be easy — and officials are willing to clamp down harder if that is what it takes to tame inflation.

“Price stability is absolutely essential for the economy to achieve its potential and sustain maximum employment over the medium term,” John C. Williams, the president of the Federal Reserve Bank of New York, said in a speech in Puerto Rico on Friday. “I want to be clear: This is not an easy task. We must be resolute, and we cannot fall short.”

Stocks fell after the release of the employment numbers, likely because investors saw them as a sign that the Fed would continue constraining the economy.

“The tremendous momentum in the economy to me suggests that we can move at 75 basis points at the next meeting and not see a lot of protracted damage to the broader economy,” Mr. Bostic said Friday.

Fed officials are closely watching wage data in particular. Average hourly earnings climbed by 5.1 percent in the year through June, down slightly from 5.3 percent the prior month. Wages for non-managers climbed by a swift 6.4 percent from a year earlier.

While that pace of increase is slowing somewhat, it is still much higher than normal — and could keep inflation elevated if it persists, as employers charge more to cover climbing labor costs.

“Wages are not principally responsible for the inflation that we’re seeing, but going forward, they would be very important, particularly in the service sector,” Jerome H. Powell, the Fed chair, said at his news conference in June.

“If you don’t have price stability, the economy’s really not going to work the way it’s supposed to,” he added later. “It won’t work for people — their wages will be eaten up.”

Inflation has been above the Fed’s target for more than a year. The Personal Consumption Expenditures index measure excluding food and energy prices, which the Fed monitors for a sense of underlying inflation trends, climbed 4.7 percent in the year through May.

And that is the least dramatic of the major inflation measures. Prices climbed by 8.6 percent in the year through May as measured by the Consumer Price Index, and the June number, set for release next week, may show further pickup.

Central bankers are increasingly worried that high costs are going to seep into consumer inflation expectations, making price gains harder to stamp out. Once workers and businesses start to believe that prices will climb rapidly year after year, they may change their behavior, seeking bigger wage increases and more regular price adjustments. That could make inflation a more permanent feature of the American economy.

The Fed wants to prevent that outcome. If it raises rates by 0.75 percentage points this month, it would bring interest rates to a range of 2.25 to 2.5 percent, and officials have signaled that they will likely push up borrowing costs by another percentage point by the end of the year.

“Supply and demand will be brought back into balance, and inflation will return to our 2 percent longer-run goal,” Mr. Williams said. “This may take some time and may well be a bumpy road.”