By Jason Lange

WASHINGTON (Reuters) - Consumer prices fell in May by the most in more than three years as households paid less for gasoline, possibly giving the U.S. Federal Reserve more room to help an economy that is showing signs of weakening.

Another government report on Thursday pointed to persistent weakness in the labor market as the number of Americans filing new claims for unemployment benefits last week rose for the fifth time in six weeks.

"The data shows that there is skepticism on the part of companies that are hiring," said Peter Cardillo, an economist at Rockwell Global Capital in New York.

The Labor Department said its Consumer Price Index dropped 0.3 percent last month after being flat in April. May's decline was the sharpest since December 2008.

Outside the volatile food and energy category, inflation pressure appeared to be modest. Core CPI climbed 0.2 percent higher, as expected, matching the increase posted in April.

Prices for U.S. government debt pared losses following the publication of the data.

While the European debt crisis poses a big threat to the global economy and President Barack Obama's November reelection bid, it has also pushed world oil prices lower.

Last month, gasoline prices fell 6.8 percent, the most in more than three years.

That amounts to something of a silver lining for Obama and the wider economy because it suggests workers will fell less stress about driving costs while having a little more money to spend on other things.

Also helping out households, natural gas prices dropped 4.1 percent in May. Prices also fell for fuel oil, while food prices were unchanged.

But the overall tenor of recent economic data has been gloomy.

A combination of the worsening debt crisis in Europe and uncertainty over whether Congress will manage to stave off the scheduled expiration of various lower tax rates at year-end, dubbed the "fiscal cliff," is souring business and consumer confidence. Job growth has slowed in the past four months, with employers adding the fewest jobs in a year in May.

Last week, initial claims for state unemployment benefits increased 6,000 to a seasonally adjusted 386,000, the Labor Department said in a separate report.

On Thursday there were sign's Europe's woes were getting worse, as Spain's 10-year bond yields hit a euro-era record of 7 percent. Yields above that rate have forced other struggling euro-area nations to seek an international bailout.

The slackening U.S. recovery has increased expectations of a further easing of monetary policy by the Fed, although economists are divided on whether the central bank will act when it holds its next policy meeting on Tuesday and Wednesday.

Overall consumer prices rose 1.7 percent year-on-year through May, the lowest reading since January and down from 2.3 percent in April. In the 12 months to May, core prices rose 2.3 percent, matching the pace clocked in April.

But while overall inflation is cooling, stickiness in the core reading could give pause to some Fed policymakers as the central bank considers possible measures to help the economy.

(Additional reporting by Lucia Mutikani in Washington and Angela Moon in New York; Editing by Padraic Cassidy)