Officials at the Federal Reserve shed further light on Friday on the divisions that led to this week’s fractured decision to lower interest rates, with views splintering over the risk posed by inflation and how concerned to be about a softening labor market.

The central bank voted to cut interest rates by a quarter of a percentage point for a third meeting in a row, a decision that was far from unanimously supported. Two members of the policy-setting Federal Open Market Committee voted for no cut, while four others expressed their disapproval by registering what is known as a “soft dissent.” That entailed them penciling in a forecast for interest rates to have ended the year at a higher level than the 3.5 to 3.75 percent now in place.

Stephen I. Miran, who joined the Fed’s Board of Governors in September after President Trump nominated him, voted instead for a larger, half-point cut, as he had done for the past two meetings.

Austan D. Goolsbee, who as president of the Federal Reserve Bank of Chicago cast one of the votes against a cut, cited on Friday his worries about inflation and his desire to have waited for more economic data before moving ahead with a reduction.

“Given that inflation has been above our target for four and a half years, further progress on it has been stalled for several months, and almost all the businesspeople and consumers we have spoken to in the district lately identify prices as a main concern, I felt the more prudent course would have been to wait for more information,” he said in a statement.

One of the complicating factors ahead of December’s decision was that officials at the Fed had access to limited data because of the government shutdown that delayed a raft of crucial economic releases. Before the latest vote, the last monthly jobs report that the central bank had in hand was from September. It showed stronger monthly jobs growth but higher unemployment.

Mr. Goolsbee, who had never issued a dissent since joining the Fed in 2023, was joined by Jeffrey R. Schmid, president of the Kansas City Fed, who also opposed a cut at the last meeting in October.

Mr. Schmid reiterated on Friday that he was concerned about lingering price pressures and questioned whether interest rates were high enough to stamp them out.

“Right now, I see an economy that is showing momentum and inflation that is too hot, suggesting that policy is not overly restrictive,” he said in a statement.

Beth Hammack, president of the Cleveland Fed who will vote on interest rates next year, echoed those concerns on Friday in a moderated discussion hosted by the University of Cincinnati, stressing that inflation has been stuck about a percentage point above the Fed’s 2 percent target for an extended period. Ms. Hammack has for many months made clear that she has not supported further cuts, suggesting there is a high bar for her to do so next year.

These divisions have forced Jerome H. Powell, the chair of the Fed, to navigate the difficult task of trying to reach a consensus among his colleagues. He did so on Wednesday by stressing that the central bank was now “well positioned to wait to see how the economy evolves,” leaving open the possibility of further action but also hinting that the central bank was done for the time being.

What will probably prompt further action is any sign that the labor market is close to cracking.

Anna Paulson, who will vote on interest rates next year as president of the Philadelphia Fed, said on Friday that she was more concerned about the labor market weakening than inflation re-accelerating, suggesting that she may support further cuts.

Mr. Powell has just three more meetings before his term as chair ends in May. President Trump has vowed to pick someone who will support substantially lower interest rates, but ongoing divisions at the Fed underscore how difficult it may be to deliver that.

Almost all of the current roster of presidents from the 12 regional reserve banks was unanimously reappointed on Thursday to new five-year terms by the board. The one exception was Raphael W. Bostic of the Atlanta Fed, who had previously announced his retirement.

That move helped to alleviate concerns that the Trump administration would try to block some of those reappointments to gain more control over the institution. Mr. Trump is currently engaged in a legal battle with Lisa D. Cook, a governor he is trying to fire over allegations that she committed mortgage fraud. The Supreme Court will hear that case in January.