WASHINGTON • For nearly a year, the Federal Reserve has been on a mission to cool down the job market to help curb the nation’s worst inflation bout in four decades.

The job market hasn’t been cooperating.

Consider what happened in January: The government said Friday that employers added a sizzling 517,000 jobs last month and that the unemployment rate dipped to 3.4%, the lowest level since 1969.

The job gain was so large it left economists scratching their heads and wondering why the Fed’s aggressive interest rate hikes haven’t slowed hiring at a time when many foresee a recession nearing.

Friday’s report added instead to the picture of a resilient U.S. labor market, with low unemployment, relatively few layoffs and many job openings. Though good for workers, employers’ steady demand for labor has also helped accelerate wage growth and contributed to high inflation.

Still, the Fed’s inflation watchers might be reassured somewhat by January’s wage data: Average hourly pay rose 4.4% last month from a year earlier, slower than the 4.8% year-overyear increase in December. And from December to January, wages rose 0.3%, below the 0.4% increase the previous month.

On top of the sizzling job growth it reported for January, the government on Friday also revised up its estimate of the gains in November and December by a combined 71,000.

January’s hiring gain, which far exceeded December’s 260,000, was broad-based across industries. A category that includes restaurants and bars added 99,000 workers. Professional and business services jobs, including bookkeepers and consultants,

rose by 82,000.

Governments added 74,000, boosted by the end of a worker strike against California’s state university system. Health care added 58,000 jobs, retailers 30,000. Construction gained 25,000 jobs. Manufacturing added 19,000.

Economists had collectively estimated that the economy added just 185,000 jobs last month.

“This is a labor market on heat,’’ said Seema Shah, chief global strategist at Principal Asset Management. It would be difficult, she suggested, “to see the Fed stop raising rates and entertain ideas of rate cuts when there is such explosive economic news coming in.”

The Fed has raised its key rate eight times since March to try to slow the job market and contain inflation, which hit a 40-year high last year but has slowed since then.

Yet companies are still seeking more workers and are hanging tightly onto the ones they have. Putting aside some high-profile layoffs at big tech companies like Microsoft, Google, Amazon and others, most workers are enjoying an unusual level of job security.

For all of 2022, the economy added a sizzling average of roughly 375,000 jobs a month. That was a pace vigorous enough to have contributed to some of the painful inflation Americans have endured.