Federal Reserve officials agreed on raising interest rates last month but differed over the rationale, leaving questions about the path of further tightening, minutes released Wednesday showed.

The minutes of the Sept. 15-16 Federal Open Market Committee meeting highlighted that officials unanimously supported raising the fed funds rate by a quarter percentage point to a range of 3.75% to 4% last month and "most" officials believed that another rate increase would likely be appropriate by year end.

In the summary of economic projections released in conjunction with the September policy decision, officials penciled in a median forecast for the federal-funds rate at 4.1% at the end of both this year and next. That implies one additional increase in 2026 and no net change in rates in 2027.

The FOMC is set to meet twice more this year, in late October and in December.

"Based on the outlook and the changing balance of risks, all participants viewed a higher target range for the federal funds rate as appropriate," according to Wednesday's minutes. "Participants judged that this would support a timelier return of inflation to the committee's 2% goal."

The minutes highlighted that "many" officials emphasized that higher rates would be "prudent on risk-management grounds," acting as insurance against inflation remaining persistently high due to the risk of supply shocks.

New York Fed President John Williams, for example, said last week that he expected just one additional rate increase this year, likely in December.

Still, the minutes said that "a number of participants" viewed higher rates as necessary based on their economic outlook, rather than as a risk-management measure. That tracks with recent remarks from Dallas Fed President Lorie Logan, who called for increasing the federal-funds rate by another half a percentage point.

"You're seeing persistent inflation, but persistent growth, and that enables the Fed to be somewhat patient, but still likely to hike down the road," says Shawn Snyder, economic strategist at Potomac Fund Management.

The odds of an October rate increase stood at just 19% after the release of the minutes on Wednesday, little changed from their levels a day prior and down from about 38% a week earlier. The probability of a hike in December stood at about 68% on Wednesday.

Officials also said they would approach each meeting with "an open mind" and that future decisions would depend on incoming data, according to the minutes.

With the latest data showing the labor market is still broadly stable and economic growth expected to be strong, that signals policymakers will likely continue to focus on their price stability mandate -- making upcoming inflation data a key driver in the committee's decisions. The September reading of the consumer price index will be a key input, for example, in the committee's decision to raise or hold rates at the Oct. 27-28 meeting.

The Bureau of Labor Statistics is set to release the latest CPI inflation data on Wednesday, Oct. 14.

Wednesday's minutes also noted that there was some discussion of the Fed's balance sheet, with a "few" officials noting that Treasury markets had been functioning smoothly, but cautioning that planning for market stress was prudent.

"They suggested strengthening the Federal Reserve's strategy, communications, and tools for addressing market dysfunction, should it occur, while limiting the Federal Reserve's footprint in the Treasury market," according to the minutes.

Fed Chair Kevin Warsh has set up a series of task forces to review a number of areas of the Fed's purview, including the balance sheet. He's said that he expects the committees to provide some feedback by the end of the year.