Jerome H. Powell, the Federal Reserve chair, is facing relentless attacks from the president, a lively campaign to replace him and divisions in his own ranks over when to cut interest rates.

Inflation has fallen sharply and as a result Fed officials have signaled they will cut rates by as much as a half-percentage point this year. Yet it has picked up a bit in the last two months and many of those policymakers, including Powell, still want to make sure that tariffs aren’t going to lift inflation much higher before they make a move.