* Jobless claims fall 32,000 last week
* Claims lowest since May 2007
* Import prices up; food price surge largest in three years
WASHINGTON, April 10 (Reuters) - The number of Americans filing new claims for unemployment benefits fell sharply last week to the lowest level in almost seven years, which could bolster views of an acceleration in job growth after a cold winter dampened hiring.
Initial claims for state unemployment benefits dropped 32,000 to a seasonally adjusted 300,000 for the week ended April 5, the Labor Department said on Thursday. That was the lowest level since May 2007, before the start of the 2007-09 recession.
"It's collaborating with the other signals we have been seeing, which is the jobs market is slowly improving. Some of the drop is normalizing from this winter's depressive effect," said Ryan Sweet, a senior economist at Moody's Analytics in West Chester, Pennsylvania.
U.S. stock index futures trimmed losses after the claims data. The dollar pared losses against the yen, while U.S. Treasury debt prices gave up some gains.
Economists had forecast first-time applications for jobless benefits falling to 320,000 for the week ended April 5.
Layoffs are trending lower and hiring is regaining some momentum after being held back by unusually cold weather, snow and ice storms in December and January.
Job growth averaged about 195,000 per month in February and March, with the unemployment rate holding at near a five-year low of 6.7 percent over that period.
The four-week moving average for new claims, considered a better measure of underlying labor market conditions as it irons out week-to-week volatility, fell to 316,250 in the week ended April 5, down 4,750 from the previous week.
The claims report showed the number of people still receiving benefits after an initial week of aid fell 62,000 to 2.78 million in the week ended March 29. That was the lowest level since January 2008.
In a separate report, the Labor Department said import prices increased 0.6 percent last month after rising 0.9 percent in February.
The increase exceeded economists' expectations of a 0.2 percent rise and was driven by food prices, which recorded their largest increase in three years. Still, there was little sign of a broader pickup in imported inflation.
In the 12 months through March, import prices fell 0.6 percent, pointing to continued weak imported inflation that is helping to keep a lid on domestic price pressures.
"There is very little price pressure. In fact, inflation is too low," Sweet said.
The lack of inflation pressures in the economy suggest the Federal Reserve could keep monetary policy very accommodative for a while even as labor market slack starts to ease.
The U.S. central bank slashed overnight interest rates to a record low of zero to 0.25 percent in December 2008 and pledged to keep them low while nursing the economy back to health.
The Fed is reducing the amount of money it is pumping into the economy each month. The minutes of its March 18-19 policy meeting published on Wednesday suggested it was not eager to start raising rates when its bond-buying program ends later this year.
Last month, import food prices jumped 3.7 percent, the biggest rise since March 2011, after falling 0.7 percent in February. Imported fuel prices rose 1.2 percent last month after advancing 5.3 percent in February.
Import prices excluding food and fuels rose 0.2 percent after slipping 0.1 percent in February.
The Labor Department report also showed export prices increased 0.8 percent in March, the largest gain since September 2012. That followed a 0.7 percent rise in February. In the 12 months through March, export prices gained 0.2 percent.
(Reporting by Lucia Mutikani; Additional reporting by Richard Leong in New York; Editing by Paul Simao)