By Jason Lange

WASHINGTON (Reuters) - Rising wages for U.S. healthcare workers had helped to drive a modest acceleration of inflation over the past year, but these gains in earnings have slowed, which could make it harder for the Federal Reserve to achieve its inflation target.

Rising prices for healthcare has been one bright spot in an economy where wage and price gains have been tepid. The Fed views an inflation rate of 2 percent as healthy, but has undershot this target the last four years.

But data on Friday appeared to confirm a trend of slowing wage gains in the sector, dimming the outlook for the faster price gains that would make the Fed more comfortable raising interest rates from very low levels.

"We'd like to see a little more inflation," New York Fed President William Dudley said on Tuesday.

Wage gains for hospital workers tend to affect prices paid months down the road, and in recent years the connection between compensation and prices has appeared tighter in the sector than in the rest of the economy, possibly because hospitals spend a relatively large share of revenues on wages.

Healthcare wages began rising sharply in 2014 as President Barack Obama's healthcare reform law fueled a surge of hiring at hospitals to treat an influx of newly insured patients.

Wages for healthcare workers were up 2.1 percent in the year through May, according to the most recent figures available for the sector released by the Labor Department on Friday.

That's about twice the rate of increase logged in mid-2014, just before wages in the sector began to pick up. The wage acceleration that began that year was followed by a rise in healthcare service inflation, from 0.7 percent in the year through September 2015 to a 12-month gain of 1.3 percent in May of this year.

The increase in healthcare costs had pushed overall inflation higher.

But job growth in the sector has cooled, as has the acceleration in wage gains, which peaked at a 2.7 percent rate in December, well above the rate in May.

Slower growth in the sector "may mean less pressure on wages, and ultimately on healthcare prices," said Larry Levitt, a healthcare economist at the Kaiser Family Foundation in Menlo Park, California.

And that could work against the Fed meeting its goal.

(Reporting by Jason Lange; Editing by Tim Ahmann and Andrea Ricci)