Federal Reserve officials have been looking for further evidence that their interest rate increases over the past two years are weighing on the economy and job market, and Friday’s employment report roundly provided that signal.

Average hourly earnings, a measure of wage growth, climbed 3.9 percent in April from a year earlier. That was both cooler than the previous reading and slightly cooler than the 4 percent economists had forecast.

That moderation came as job gains slowed, the unemployment rate ticked up slightly and average weekly hours nudged down. The overall picture was one of a labor market that remains solid but is gradually slowing — exactly what officials at the Fed have been looking for.

Central bankers generally embrace a strong job market: One of their two mandates from Congress is to foster maximum employment. But when inflation is rapid, like it has been since 2021, officials worry that a hot labor market could help to keep price gains elevated. If employers are competing for workers and paying more, they are likely to also try to charge more, the theory goes. And workers who are earning slightly bigger paychecks may have the wherewithal to pay more without pulling back.

Given that, Fed officials have been keeping an eye on the job market as they contemplate their next steps on interest rates. At the Fed’s policy meeting this week, officials kept interest rates at 5.3 percent, the highest level in more than two decades. The central bank started 2024 expecting to cut rates several times, but those plans have been delayed by surprisingly stubborn inflation.

While inflation is the main thing determining when and how much borrowing costs can come down, Jerome H. Powell, the chair of the Federal Reserve, made it clear this week that central bankers are also watching what happens with hiring and pay.