(Reuters) -Slowly cooling inflation and a U.S. job market that remains strong but at risk of deteriorating give a green light for more interest-rate cuts in coming months, Federal Reserve policymakers indicated in remarks on Thursday, even as one suggested that skipping a move in November may be in order.

Data showed consumer price inflation edged down to 2.4% in September from a 2.5% pace the prior month, and weekly claims for unemployment insurance surged in a development that economists attributed in part to a temporary blow from Hurricane Helene.

With inflation now near the Fed's 2% goal, and the unemployment rate now at 4.1%, "we're trying to freeze the dual-mandate performance basically exactly where it is right now," Chicago Federal Reserve Bank President Austan Goolsbee told CNBC, referring to the Fed's two mandates of price stability and full employment.

"The vast majority (of Fed policymakers) believes that over the next 12 to 18 months, conditions continue to slowly and gradually improve to something like target, and rates gradually come down a fair amount to something well below where they are today," he said.

At an event at Binghamton University, New York Fed President John Williams said the timing and pace of rate cuts will depend on the data, but "based on my current forecast for the economy, I expect that it will be appropriate to continue the process of moving the stance of monetary policy to a more neutral setting over time."

Financial markets reflected heavy bets the Fed would deliver a quarter-point rate cut at next month's policy meeting and at each meeting through the first half of next year, with the policy rate likely going no lower than 3.5% by year's end. At midday, rate-futures pricing put about a 17% chance on no rate cut at all in November.

"I'm definitely open to that," Atlanta Federal Reserve Bank President Raphael Bostic told the Wall Street Journal, referring to a potential November rate-cut pause.

He said that last month he had penciled in just one 25 basis-point rate cut over the Fed's two final meetings of the year, a view also reflected in the projections of a half dozen of his fellow policymakers. There are 19 Fed policymakers in total, and a slight majority had written down projections that pointed to quarter-point cuts at each of the remaining 2024 meetings.

The Fed last month cut its policy rate by a bigger-than-expected half-of-a-percentage point.

Policymakers have said that was a "recalibration" of policy to better align borrowing costs with a big drop in inflation and bit of slowing in the job market since the central bank stopped raising rates back in July 2023, and should not be seen as suggesting the future pace of rate cuts.

Minutes of the Fed's meeting released on Wednesday showed the decision had been a close call, and Goolsbee on Thursday said he expected more close-call meetings ahead.

The short-term benchmark rate is now in the 4.75%-5.00% range. On Thursday, futures contracts that settle to the Fed's policy rate were pricing in a better-than-even chance of a policy rate in the 3.5%-3.75% range by June of 2025, with a small chance of it going lower.

Economists had expected annual inflation to slow to 2.3% in September. From a month earlier, the CPI rose 0.2%, more than the 0.1% forecast by economists, boosted by shelter and food costs.

"The larger-than-anticipated gain in the September consumer price index doesn't signal a reacceleration in inflation, nor will it deter the Federal Reserve from cutting interest rates by 25 basis points at its November meeting," wrote Oxford Economics' Chief U.S. Economist Ryan Sweet. "The Fed needs to continue to normalize interest rates to keep the economy on the path toward a soft landing."

San Francisco Fed President Mary Daly late on Wednesday said that without a large reduction in rates she had been worried tight monetary policy could injure the labor market or break the economy. She now feels that smaller rate cuts ahead will likely be appropriate, with one or two reductions to come over the Fed's last two meetings of the year.