WASHINGTON, Jan 31 (Reuters) - U.S. labor costs rose less than expected in the fourth quarter, leading to the smallest annual increase in two years, signs of moderating wage inflation that could give the Federal Reserve room to start cutting interest rates by June.

The Employment Cost Index (ECI), the broadest measure of labor costs, increased 0.9% last quarter after advancing 1.1% in the July-September period, the Labor Department's Bureau of Labor Statistics said on Wednesday. Economists polled by Reuters had forecast the ECI gaining 1.0%.

Labor costs increased 4.2% on a year-on-year basis, the smallest gain since the fourth quarter of 2021, after rising 4.3% in the third quarter. Annual compensation growth peaked at 5.1% in 2022.

The labor market is gradually easing, with government data on Tuesday showing there were 1.4 job openings for every unemployed person in December. Though this ratio was steady from November, it has declined from two jobs in March 2022.

Fed officials are expected to keep interest rates unchanged at the end of a two-day policy meeting on Wednesday against the backdrop of a resilient economy, which is being anchored by the labor market through consumer spending.

Financial markets have lowered the odds of a rate cut in March to below 50%. Since March 2022, the U.S. central bank has raised its policy rate by 525 basis points to the current 5.25%-5.50% range.

The ECI is widely viewed by policymakers and economists as one of the better measures of labor market slack and a predictor of core inflation because it adjusts for composition and job-quality changes. (Reporting By Lucia Mutikani; Editing by Andrea Ricci)