Consumer prices fell for the first time in a year last month and the closely watched core inflation rate posted its smallest annual gain since 1966, pointing to a lack of price pressure as the economic recovery gathers steam.

The Consumer Price Index unexpectedly slipped 0.1 percent in April, the Labor Department reported on Wednesday, which analysts said should allow the U.S. Federal Reserve to focus on supporting growth, especially as Europe's debt crisis looks set to slow economies there.

An industry report released separately showed demand for loans to buy homes sank 27.1 percent to a 13-year low last week after the expiry of a home buyers tax credit, suggesting a recovery in housing will be painfully slow.

The latest CPI data confirms that the Fed has a free hand to concentrate on growth, said Alan Ruskin, head of currency strategy at RBS Global Banking & Markets in Stamford, Connecticut.

The April CPI was pulled down by declining energy costs. Consumer prices rose 0.1 percent in March and markets had expected a similar gain in April.

The core inflation rate, which excludes volatile food and energy costs, was flat last month. Over the past 12 months, core inflation has risen just 0.9 percent, the smallest gain in more than 44 years.

Some analysts said the latest data reflected weakness in the economy.

The elevated unemployment rate continues to restrain consumer spending, affording businesses limited ability to raise prices, said Jim Baird, chief investment strategist at Plante Moran Financial Advisors in Kalamazoo, Michigan.

Without substantial increases in employment, we are running the risk of not only low inflation, but the potential of further disinflation.

The Fed cut benchmark overnight lending rates to near zero percent in December 2008 and has vowed to keep them extraordinarily low for an extended period to nurse the economy back from its worst downturn since the 1930s.

While the economy has grown for three straight quarters and employers have added jobs for four months in a row, the unemployment rate stands at 9.9 percent.

MARKETS IGNORE DATA

U.S. financial markets were little moved by the data, remaining preoccupied with Europe's debt troubles. Major U.S. stock indexes were down more than 1 percent in late morning, while prices for government resumed their advance as stocks slid. The U.S. dollar fell against the euro on speculation surrounding the European Central Bank.

While analysts generally believe the fiscal problems in Europe will have a minimal impact on the U.S. economy, Paul Volcker, the former Fed Chairman who is a White House economics adviser, said the European crisis showed the risks for the nation if it did not get its budget deficit under control.

The U.S. government's record economic stimulus package helped push the budget deficit last year to $1.4 trillion, roughly 10 percent of gross domestic product. There have been fears that the budget deficit and the vast amounts of money pumped into the economy by the Fed could stoke inflation.

For now, those concerns are muted as substantial slack in the domestic economy is keeping price pressures subdued.

Last month, overall consumer prices fell as energy and gasoline prices posted their largest declines since March 2009. Food prices rose moderately for a second straight month.

And core consumer prices were held back by new vehicle and shelter costs, which were unchanged. Clothing prices fell, while medical care costs rose marginally.

A glut of homes on the market is keeping rental costs in check, a trend likely to continue amid expectations the housing market will struggle to recover without government incentives.

Homebuyers looking to cash in on federal tax credits had to have signed contracts by April 30 and must close on their loans by June 30. The week ended May 14 was the second straight week that demand for loans to buy homes fell, after three straight weeks of sharp gains ahead of the April 30 deadline.

It's disturbing, said John Canally, economist at LPL Financial in Boston. It seems that every other data point for housing is pretty good -- high affordability, low interest rates, relatively low inventory, home prices are up -- so I'm leaning toward the hangover from the tax credit but I'm going to need to see a couple of more weeks of data.

Demand to refinance mortgages, however, jumped 14.5 percent last week to a nine-week high, the Mortgage Bankers Association said. Overall loan requests fell 1.5 percent, it said.

But in another sign of problems plaguing the housing recovery, the Mortgage Bankers Association reported on Wednesday that one in every seven U.S. households with a mortgage ended the first quarter behind on payments or in foreclosure. Although the rate of new foreclosure actions has slowed, the number of problem loans signals the long path to recovery faced by the housing market.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ U.S. inflation graphic: http://link.reuters.com/keh25k U.S. mortgages graphic: http://link.reuters.com/naf25k

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(Additional reporting by Lynn Adler; Editing by Leslie Adler)