-- Inflation in the U.S. is slowing toward the Federal Reserve's 2% target level thanks in part to a run of interest rate hikes instituted by the central bank, according to Fed Governor Christopher Waller.

In remarks on Tuesday, Waller said the Fed's restrictive monetary policy stance is "helping to cool off aggregate demand," adding that softer inflation data for April suggests that "progress toward 2% has likely resumed" after appearing to have stalled earlier in 2024.

Businesses also seem to be in less need to fill vacancies and offer relatively high starting salaries, which could lead to a moderation in wage increases and broader price pressures, Waller said.

"Central bankers should never say never, but the data suggests that inflation isn't accelerating, and I believe that further increases in the policy rate are probably unnecessary," he noted.

The comments come after several of Waller's Fed colleagues sounded a largely cautious note on Monday, flagging that they have yet to see sufficient evidence that a cooldown in inflation will be long-lasting. As a result, they largely hinted that borrowing costs will need to stay at their currently elevated level of 5.25% to 5.5% until there is more proof that price pressures are abating.

The Fed's next policy meeting is slated for June 11-12. Traders are widely betting that officials will leave rates unchanged at the gathering.