Kevin M. Warsh made one thing abundantly clear in his first weeks as chairman of the Federal Reserve. With inflation running for five years above the central bank’s 2 percent target, the Fed would put achieving price stability over just about everything else.

A solid labor market gives Mr. Warsh the space to do so. Data released on Thursday is expected to show monthly jobs growth of 110,000 positions in June as the unemployment rate stayed stable at 4.3 percent.

It would mark the fourth straight month that employers added more than 100,000 monthly jobs, reversing muted jobs growth last year. Despite the robust clip of hiring, wages have not picked up significantly, suggesting that the labor market is not a source of inflationary pressure at the moment. Moreover, any raises have been more than offset by the acceleration in inflation in recent months.

Since April, consumer prices have been growing at the fastest pace in three years, reflecting a surge in energy expenses caused by the war with Iran. In recent weeks, however, oil prices, and those for gasoline, shipping and other categories, have fallen sharply amid the emergence of a deal to end the conflict.

If that deal holds, it’s possible that the worst of the recent inflation shock might soon be over. Speaking on Wednesday, Mr. Warsh noted that inflation risks had moderated in recent weeks.

“Expectations of inflation over the first four weeks of this period, they’ve come down. Inflation risks have come down,” Mr. Warsh said at the European Central Bank’s annual gathering of international policymakers and economists in Sintra, Portugal.

Still, the Fed’s problems look poised to linger for a lot longer.

Underlying inflation measures — ones that strip out volatile items like food and energy and track the rate that prices would rise based on supply and demand in the economy as a whole — are still way too high for the Fed’s liking. There are reasons to be optimistic that after the recent run-up in prices caused by the Iran war reverse course, underlying inflation will begin to ease.

The effect of President Trump’s tariffs on prices has finally begun to fade. Housing-related inflation has firmed in recent months but is expected to decelerate again over time. Wage growth has stayed muted despite the recent stabilization of the labor market. And higher productivity from the proliferation of artificial intelligence, if sustained, could eventually help tame prices.

But all of this could take time to materialize, leaving policymakers at the Fed in a difficult spot. The question now confronting Mr. Warsh is whether interest rates will need to be raised in order to make good on his price stability pledge, something he said at his first news conference in mid-June would be pursued “unambiguously and unanimously.”

Mr. Warsh declined to say on Wednesday whether the Fed would consider raising rates at its next meeting at the end of the month, reflecting his opposition to the central bank sending signals about the outlook. Instead, the only thing he was explicit about was the Fed’s commitment to getting inflation down.

“If there were people in households or the business sector or the financial markets who thought that this central bank was going to be comfortable with an inflation objective above 2 percent, well, I guess they’d be disappointed,” he said.

“We’re going to deliver price stability in the U.S.,” Mr. Warsh added, noting that “the tactics, the strategy, and the rest, that’s still to come.”

But the vacuum left by Mr. Warsh’s approach has already started to be filled by other Fed officials. Beth Hammack, who as president of the Cleveland Fed is one of 12 voting members on the policy-setting committee this year, on Tuesday suggested that rates at the current 3.5 percent to 3.75 percent level were not weighing heavily on the economy.

“If inflation continues to persist at these elevated levels and I don’t see any restraint from policy, we may need to raise rates to bring that policy restraint in and to bring inflation back down,” she said in an interview with CNBC.

Neel Kashkari, who is another voting member this year as president of the Minneapolis Fed, has penciled in one quarter-point increase by year-end, in line with market expectations.