WASHINGTON (Reuters) - U.S. consumer prices rose slightly more than expected in September, but the annual increase in inflation was the smallest in more than 3-1/2 years, potentially keeping the Federal Reserve on track to cut interest rates again next month.

The consumer price index increased 0.2% last month after gaining 0.2% in August, the Labor Department's Bureau of Labor Statistics said on Thursday. In the 12 months through September, the CPI climbed 2.4%. That was the smallest year-on-year rise since February 2021 and followed a 2.5% advance in August.

Economists polled by Reuters had forecast the CPI edging up 0.1% and rising 2.3% year-on-year. The annual increase in inflation has slowed from a peak of 9.1% in June 2022.

Together with a significant moderation in the inflation measures tracked by the U.S. central bank for its 2% target, that allowed the Fed to shift focus to the labor market and deliver an unusually large 50 basis points rate cut in September.

Minutes of that meeting published on Wednesday showed a "substantial majority" of policymakers supported beginning an era of easier monetary policy, but there appeared even broader agreement that the initial move would not commit the Fed to any particular pace of rate reductions in the future.

The first rate reduction since 2020 lowered the central bank's policy rate to the 4.75%-5.00% range. The Fed hiked rates by 525 basis points in 2022 and 2023.

Labor market resilience and solid consumer spending have, however, forced investors to abandon hopes for another half-percentage point rate reduction next month.

The economy added the most jobs in six months in September and the unemployment rate fell to 4.1% from 4.2% in August. Revisions to national accounts data last month from 2019 through the second quarter of this year also showed that the economy was in much better shape than previously estimated.

There are also some pockets of stickiness, especially rents, which are slowing the pace of cooling in underlying inflation.

Excluding the volatile food and energy components, the CPI increased 0.3% in September after rising 0.3% in August. In the 12 months through September, the so-called core CPI advanced 3.3%. That followed a 3.2% gain in August.

Early on Thursday, financial markets saw a roughly 76% probability of a 25 basis points rate cut at the Fed's Nov. 6-7 policy meeting, according to CME Group's FedWatch Tool. The odds of rates being unchanged were at about 24%.