Officials at the Fed expected inflation to surge because of the war in Iran, which began in February. Without a deal to end the conflict, energy prices have stayed elevated, pushing up prices for food and transportation.

Their primary concern is that prices might rise in goods and services not directly exposed to the war, especially if that is paired with a shift in how Americans view the extent of the inflation problem. If people start to question whether inflation is going to eventually be low and stable again, that would make it far more difficult for the Fed to stamp out price pressures. According to data the New York Fed released on Monday, consumers still expect inflation to be elevated through the end of 2026 before tapering off in the coming years.

The relatively benign increases in core prices in May will also give officials some comfort that the war with Iran is not sowing a more persistent inflation problem. But it does not signal that the central bank is entirely in the clear. The longer the conflict lasts, the higher the odds the problem of sticky price gains develops. And there is little indication that the labor market is weakening, suggesting that businesses may still have some leeway to raise prices on consumers.

Officials at the Fed have soured on rate cuts against this backdrop. In fact, many central bank officials have talked about the possibility that rates may need to rise at some point to bring inflation back to the central bank’s 2 percent target.

Kevin M. Warsh, who will preside over his first meeting as Fed chair next week, will be tasked with forging a consensus among his new colleagues over the path forward for rates while also dealing with repeated calls from President Trump for lower them.

In the wake of the May inflation data, financial markets tracking investors’ expectations for rates showed not only no reduction in the coming months, but a rate increase in December.