Yet annual price increases slowed to 1.6 percent on a core basis in March, taking the Fed further away from its stubbornly elusive goal of 2 percent inflation. Weak inflation raises the risk of economy-damaging deflation, so the central bank aims to keep prices growing at a slow and steady rate.

That disconnect poses a serious policy challenge. If officials cut rates to lift prices against a backdrop of strong growth, they risk fueling financial excess and looking like they have caved to political pressures.

Should inflation slip too low for too long, on the other hand, businesses and consumers could come to expect permanently slower gains and behave accordingly. That would make it harder for the Fed to ever achieve its 2 percent goal.

Charles L. Evans, the president of the Federal Reserve Bank of Chicago, has indicated that rate cuts are possible if inflation falls too low and stays there. “Anything that’s sustainable, that looks like it’s moving downward, not upward, I would be extremely nervous about,” Mr. Evans told The Wall Street Journal in April. “I would definitely be thinking about taking out insurance in that regard.”

The full committee will not release fresh economic projections until after its June meeting, but Jerome H. Powell, the Fed chairman, could flesh out what conditions would merit a precautionary cut and explain whether such a move is becoming more likely during his postmeeting news conference.

Subtle statement tweaks could also provide the setup for a future shift. Officials could use their release to highlight lower inflation as a real risk rather than a transitory miss, said Neil Dutta, the head of economic research at Renaissance Macro Research.

“If they sound more dovish on inflation, more worried about where inflation is going, that would tee up the idea that there could be a policy response,” Mr. Dutta said.