(Reuters) - Federal Reserve officials, buffeted in recent months by concerns the economy might again overheat, got relief on Friday when jobs data for April showed a marked cooling in wage growth and a pace of hiring in line with levels seen before the COVID-19 pandemic.

The gain of 175,000 payroll jobs last month was the lowest in more than a year, while the 3.9% annual change in average hourly earnings was the smallest since May of 2021 and continued what has been a steady decline towards the mid-3% range that policymakers feel is consistent with their 2% inflation target.

Fed Governor Michelle Bowman, who has been among the more ardent voices on the steps needed to control inflation, said after the release of the data that her outlook remained "that inflation will decline further with the policy rate held steady."

Bowman, along with all other members of the central bank's policy-setting committee, voted earlier this week to keep the policy interest rate steady in the current 5.25%-5.50% range.

Traders responded to the jobs data by adding to bets that the Fed will deliver its first rate cut this year in September and likely follow with a second quarter-percentage-point cut in December. Both probabilities had been sliding recently as inflation data ran hotter than anticipated and Fed officials at their April 30-May 1 meeting noted the lack of recent progress in lowering the pace of price increases.

Other data, such as a slowdown in overall output, was dismissed as masking strong underlying demand, while a weak productivity figure for the first three months of the year raised the possibility that a key force helping to slow inflation may be of less assistance in the months ahead.

But Fed Chair Jerome Powell in his post-meeting press conference on Wednesday cited an array of indicators he felt showed the labor market moving into a better alignment between the hiring demands of employers and the number of people looking for jobs.

Data on job openings, and the rate at which workers are quitting jobs and at which firms are hiring workers, have all indicated some softening in the labor market.

In surveys of workers and businesses, answers to questions about the ease of finding jobs or filling positions "have come back down to pre-pandemic levels," Powell said.

The weaker-than-expected jobs gain in April was a wide miss from the 243,000 additional positions expected by economists in a Reuters poll.

But it also hit a spot that Powell and his colleagues may see as bolstering their hopes of a "soft landing" in which inflation is tamed without a major hit to employment or a painful recession.

While the jobless rate rose one-tenth of a percentage point to 3.9%, it remained below the 4.1% figure Fed officials at the median feel is aligned with their 2% inflation target.

The jobs growth last month also remained close to the monthly average of 183,000 seen in the decade before the pandemic, and above the roughly 100,000 that policymakers feel is needed to accommodate population growth.

"A 175,000 per month pace is still plenty good enough to absorb new entrants into the labor force and sustain a low unemployment rate," said Thomas Simons, senior U.S. economist at Jefferies.