The red-hot labor market cooled some in March, with hiring gains moderating and wage growth easing as more workers sought jobs.

Employers added 236,000 workers last month, a historically strong gain but the smallest in more than two years, the Labor Department said Friday. The unemployment rate ticked down to 3.5%.

More Americans jumped into the labor market in March, helping take pressure off wage increases. Average hourly earnings rose 4.2% last month from a year earlier, the smallest annual gain since mid-2021 when inflation was surging.

Steady hiring growth last month could keep the Federal Reserve on track to consider raising interest rates again at its meeting in early May. But slower wage gains could also allow officials to hint at a pause after that. Fed officials have signaled they will pay close attention to other measures of economic activity including bank lending conditions as they debate their next move.

Bond yields and stock futures rose after the jobs report. The stock market was closed for Good Friday, and bond and futures markets closed early.

The March jobs numbers add to others indicating the U.S. economy has slowed after showing surprising strength at the start of the year. Consumer spending—the primary driver of growth—also rose more modestly in February and still-high inflation ebbed.

The labor market remains solid a year after the Fed began aggressively raising interest rates to tame high inflation. Job gains, though, are less broad-based than during the height of the pandemic rebound in 2021 and 2022.

Restaurants, bars, hospitals, and nursing homes helped drive March’s job growth. Meanwhile, employers in sectors that boomed earlier in the pandemic as Americans were stuck at home—including construction, manufacturing, and retail—cut jobs last month.

Average weekly hours also ticked down in March, suggesting a modest reduction in labor demand.

“The great labor market machine is finally slowing down some, but it’s still got a lot of strength left,” said Robert Frick, corporate economist at Navy Federal Credit Union.

Hiring gains at many in-person services businesses are helping offset cuts at large companies in industries such as technology, finance, and entertainment. Zoom Video Communications Inc. is laying off 1,300 employees, or 15% of its staff. Goldman Sachs Group Inc. has said it planned to cut 3,200 jobs. Walt Disney Co. began laying off workers in late March.

The jobs report reflects March hiring trends as banking system turmoil erupted last month when federal regulators closed a regional bank experiencing a huge outflow of deposits and developed plans to halt a run on another bank.

The crisis raised concerns that a potential pullback in lending could slow the economy further. Small businesses and consumers might find it harder to get loans, which could ultimately result in layoffs. Workers, meanwhile, could hesitate to search for new jobs.

Fed policymakers raised rates by a quarter-point at each of their two meetings this year, most recently in March to a range between 4.75% and 5%. The Fed has been trying to slow investment, spending, and hiring to combat inflation.

Slowing wage growth during the first quarter could comfort Fed officials who have worried that strong earnings gains would fuel continued inflation above the central bank’s 2% target. The personal consumption-expenditures price index, the Fed’s preferred inflation gauge, rose 5% in February from a year earlier, down from a June 2022 peak of 7%.

Overall private-sector wage growth has been slowing broadly. Average hourly earnings on a three-month annualized basis returned to pre-pandemic levels, rising 3.2% in March and down from 4.9% in December.

Those slower growth rates should signal to the Fed “that the kindling for future inflation is dwindling,” said Omair Sharif of Inflation Insights LLC, an advisory firm. “This is undoubtedly going to be looked at as good news by the Fed, as they continue to worry that higher labor costs are the main” driver of non-housing, service-sector inflation.

Wage gains continue to run above the pre-pandemic pace in some pockets of the economy. Earnings were up 6.1% in March from a year earlier in leisure and hospitality, nearly twice the February 2020 pre-pandemic rate.

“We’re starting from such a significant position of strength that you can weaken quite a bit and still have labor-market conditions that are tight and that are supportive of continued upward inflation pressure,” said Thomas Simons, economist at Jefferies.

The still-strong job market is helping workers whose employment prospects were hard hit by the onset of the pandemic three years ago. The unemployment rate for Black workers fell to 5% in March—a record low. That was 1.8 percentage points above the rate for white workers, the narrowest gap on record.

The tight labor market continues to make it difficult for employers to bulk up their staffing levels.

G & B Electric Inc., which installs electrical systems in buildings throughout southeast Michigan, is seeking to add about 15 workers to its staff of 62, said Jim Gierlach, the company’s owner.

Though the business has been able to find electrical apprentices, it has been a challenge to fill other roles. A job opening for a price estimator has gone unfilled for about a year. Experienced electricians are also difficult to come by, he said.

Mr. Gierlach has raised wages an average of 10% over the past year to attract workers and keep existing ones from leaving for jobs at other companies. His workers also need raises to help tackle higher prices, he said.

“They and their families are getting pinched by inflation in every aspect of life, whether it’s food or travel or housing, so they’re asking for more money,” he said.

In Green Bay, Wis., the jobless rate is 2.5%, even lower than the national rate. Many employers in the region are still struggling to tap talent, said Matt Sullivan, who co-owns an Express Employment Professionals recruitment office in Green Bay.

Manufacturers in northeast Wisconsin are hot to hire workers, he said. Other companies are trying to fill positions in engineering, sales, human resources, and finance.

With such a small pool of unemployed job seekers to fill the abundant openings, Mr. Sullivan is busy seeking to recruit workers who already have jobs.

“The secret sauce is you have to pursue the people who are currently employed,” he said.