June 5 (Reuters) - The U.S. services sector snapped back into growth mode in May after a short-lived contraction the month before, with a measure of business activity improving by the most in three years, according to a survey published Wednesday that may buttress the Federal Reserve's wariness of a shift to interest rate cuts.

The Institute for Supply Management said its nonmanufacturing purchasing managers index rose to 53.8 last month from 49.4 in April. May's reading, the highest since August, topped the estimates of all 59 economists in a Reuters poll that had pegged the median expectation at 50.8, just above the 50 level that separates growth from contraction.

The report's business activity index shot up 10.3 points, the largest rise since March 2021 and vaulting it to 61.2, the highest level since November 2022.

New orders growth reaccelerated after easing in the prior two months and a measure of services input costs eased. Employment, while improved from April's four-month low, remained in contraction territory at 47.1.

The stronger-than-expected services reading stood in contrast to ISM's report on the manufacturing sector released on Monday, which showed factory activity contracted for the second straight month in May.

Indeed, incoming data over the last month has generally failed to meet economists' projections, adding to evidence that the Fed's 525 basis points of interest rate increases since March 2022 is finally weighing on an economy that has proven stubbornly resilient.

But with services accounting for the vast majority of U.S. economic output, the upside surprise may reinforce a hesitance to shift toward interest rate cuts among Fed policymakers who have been rattled by stiffer-than-expected inflation so far this year.

The Fed next meets June 11-12 and is expected to leave rates unchanged, but the central bank will release updated projections from officials for growth, unemployment, inflation and the appropriate policy setting over various time horizons.

When those projections were last updated in March, the median expectation among policymakers was for three rate cuts of a quarter-percentage-point each by the end of this year. That is certainly no longer the case, and the debate among investors now centers on whether the Fed will deliver two rate cuts or just one this year.

(Reporting By Dan Burns; Editing by Chizu Nomiyama)