(Reuters) -Federal Reserve policymakers looking for signs that inflation is back on track to their 2% goal got that in spades Wednesday as a government report showed consumer prices unexpectedly fell in June, bolstering the case for an interest rate cut in September.

The consumer price index slid 0.1% last month after being unchanged in May, the Labor Department's Bureau of Labor Statistics said on Thursday, and the year-over-year rise cooled to 3%, the lowest reading in a year.

Traders reacted swiftly, pricing in about an 85% chance of a September rate cut after the report, up from about 70% earlier, and also boosting bets on second rate cut in December. They also priced in an increasing, but still less than 50-50, chance that the Fed will squeeze in a third rate cut by year's end.

"If we have another good inflation report in August, then I think we could see at least two rate cuts this year, possibly three," said Peter Cardillo, chief market economist at Spartan Capital Securities.

The Fed next meets at the end of this month, and traders see less than a 10% chance of a rate cut then. Fed Chair Jerome Powell on Tuesday said that inflation data at this point didn't give him the confidence to cut rates yet, but that the central bank would do so when it was needed.