(Fixes typo in headline)

By Lucia Mutikani

WASHINGTON (Reuters) -U.S. consumer prices rose moderately in July and the annual increase in inflation slowed to below 3% for the first time since early 2021, further strengthening expectations the Federal Reserve will cut interest rates next month.

The report from the Labor Department on Wednesday added to a mild increase in producer prices in July in suggesting that inflation was firmly back on a downward trend. That should allow the U.S. central bank to focus more on the labor market amid growing concerns of a sharp slowdown.

"The relay race to Fed cuts is on," said Lindsay Rosner, head of multi-sector fixed income at Goldman Sachs Asset Management. "The Fed is on track to cut some amount in September, and we've got two more legs of this race to go."

The consumer price index increased 0.2% last month after falling 0.1% in June, the Labor Department's Bureau of Labor Statistics said. The rise was in line with economists' expectations. A 0.4% increase in shelter, which includes rents, accounted for nearly 90% of the rose in the CPI. Shelter costs increased 0.2% in June.

Food prices gained 0.2%, matching June's rise. Gasoline prices were unchanged after falling for two straight months. In the 12 months through July, the CPI increased 2.9%. That was the first sub-3% reading and smallest gain since March 2021. Consumer prices advanced 3.0% on a year-on-year basis in June.

Annual consumer price growth has moderated considerably from a peak of 9.1% in June 2022 as higher borrowing costs cool demand. While still elevated, inflation is moving towards the Fed's 2% target.

The odds of a half-percentage-point rate cut at the Fed's Sept. 17-18 policy meeting are around 59%, with the remainder of bets on a quarter-percentage-point drop, according to CME Group's FedWatch tool. The rate pricing mostly reflects the jump in the unemployment rate to near a three-year high of 4.3% in July.

Economists, however, argue the labor market would have to deteriorate considerably for the central bank to deliver a 50-basis-point reduction in borrowing costs. The fourth straight monthly increase in the jobless rate was mostly driven by an immigration-induced rise in labor supply rather than layoffs.

The Fed has maintained its benchmark overnight interest rate in the current 5.25%-5.50% range for more than a year, having raised it by 525 basis points in 2022 and 2023.

Excluding the volatile food and energy components, the CPI rose 0.2% in July after rising 0.1% in June. In the 12 months through July, the core CPI advanced 3.2%.

That was the smallest year-on-year increase since April 2021 and followed a 3.3% gain in June.

"Unless the global economy experiences another shock, the Fed will most likely cut rates by a quarter percent in September," said Jeffrey Roach, chief economist at LPL Financial. "The probability of the Fed cutting by a half percent is still elevated since investors are still somewhat skittish from recent events."