By Michael S. Derby and Lindsay (NYSE:) Dunsmuir

(Reuters) -Federal Reserve officials, encouraged by recent data, are looking for more confirmation that inflation is sustainably cooling and for any warning signs from a still-strong labor market as they steer cautiously toward a potential policy easing later this year.

“I expect interest rates to come down gradually over the next couple of years, reflecting the fact that inflation is coming back to our 2% target and the economy is moving in a very strong sustainable path,” New York Fed President John Williams said on Tuesday in an interview on the Fox Business television channel.

But he declined to say when that could occur. Financial markets are currently pricing in a first rate cut in September.

“I’m not going to make a prediction” about the exact path of policy. What happens “depends on how the data evolves,” he said, adding “I think that things are moving in the right direction” for an eventual easing.

To Richmond Fed President Thomas Barkin, the key will be for price pressures to ease persistently in services as well as in goods.

“We are clearly on the back side of inflation,” Barkin told MNI in a webcast interview, adding that he found recent data showing consumer prices did not rise at all from April to May “encouraging.” Still, he said, the choppiness in data since last year means the policy path ahead is not clear.

“We will learn a lot more over the next several months and I think we are well positioned from a policy standpoint to react,” he said.

The pair’s comments were their first public remarks since last week’s Fed policy meeting, when the central bank kept its benchmark interest rate in the 5.25%-5.50% range. The Fed also released updated economic projections that showed its officials had pared back their expectations for rate cuts this year, to one from the three seen in March, after stronger-than-expected inflation data in the first months of 2024.

Most analysts equate fewer rate cuts with a later start to them, particularly after Fed Chair Jerome Powell said the first rate cut will be “consequential” because it could reset market expectations.

For the Fed, “job number one is to make sure that we get inflation back to 2%,” Williams said on Tuesday, as he rejected the idea that the central bank would tolerate inflation holding around the 3% level.

He also weighed into the debate that some recent data might be overstating what have been robust job market gains. Overall, the data “tell me convincingly we still have a very strong labor market and we’re seeing some slowing in hiring,” Williams said. But he acknowledged some parts of the job data may be “overstated,” adding that it will take time to confirm it.