Federal Reserve officials on Friday outlined the case for an interest-rate cut, making clear in their first public remarks since the central bank chose to leave policy unchanged this week that inflation and rising global risks are weighing heavily on their minds.

Neel Kashkari, the president of the Federal Reserve Bank of Minneapolis, said in an essay posted online that he had pushed for a 0.5 percentage point rate cut at the central bank’s June meeting on Wednesday, motivated by worries that inflation was too low. Mr. Kashkari does not vote on policy this year and could not dissent from the decision to hold rates steady, but he still participates in the discussions.

James Bullard, the president of the Federal Reserve Bank of St. Louis and a dissenting vote in the decision to keep rates steady, said he wanted to move more quickly to get ahead of any future weakness. Mr. Bullard’s “no” vote was the first dissent during Jerome H. Powell’s tenure as Fed chair, a position he took on in February 2018.

Cutting rates now “would provide insurance against further declines in expected inflation and a slowing economy subject to elevated downside risks,” Mr. Bullard said in a statement released on Friday. “Even if a sharper-than-expected slowdown does not materialize, a rate cut would help promote a more rapid return of inflation and inflation expectations to target.”