* Jobless claims fall 1,000 last week
* Four-week average of claims falls 5,250
* Trade deficit widens to $51.8 bln in March
* Stronger imports hint at firmer domestic demand
WASHINGTON, May 10 (Reuters) - The number of Americans submitting new applications for jobless benefits edged down last week, easing concerns the labor market was deteriorating after surprisingly weak employment growth in April.
Another report on Thursday showed the U.S. trade deficit widened in March, with exports surging to a record high and a rise in imports highlighting the economy's firming underlying demand.
Together, the reports indicated the economy remains on a moderate growth path, despite the softer jobs growth and signs the service sector slowed in April.
"The slowdown we have seen in economic activity and employment growth during in the past two months may be in the rear view mirror," said Millan Mulraine, senior macro strategist at TD Securities in New York.
New claims for state unemployment benefits slipped 1,000 last week to a seasonally adjusted 367,000, the Labor Department said. Economists who had expected claims to rise to 369,000 said the decline suggested seasonal distortions that had led to a spike in applications last month was probably over.
The four-week moving average for new claims, considered a better measure of labor market trends, fell 5,250 to 379,000.
Separately, the trade gap widened 14.1 percent to $51.8 billion in March, the biggest jump in nearly a year, as a surge in imports swamped a rise in exports, which hit a record high.
Imports grew 5.2 percent, the biggest gain since January. That jump was consistent with a rise in consumer spending seen during the first quarter.
Exports had another good month, rising 2.9 percent, suggesting the global economy had not slowed as much as people had feared.
"With imports for everything surging, it is hard to argue that the economy is softening," said Joel Naroff, chief economist at Naroff Economic Advisors in Holland, Pennsylvania.
While a widening trade deficit is a drag on gross domestic product, the details of the trade report were broadly in line with the government's assumptions when it made its first GDP estimate last month.
Still, the government's gauge of first-quarter GDP growth is expected to be lowered to an annual pace of about 1.9 percent from 2.2 percent because of a smaller-than-expected rise in wholesale inventories in March reported on Wednesday.
LABOR MARKET IMPROVING
The claims data and bargain-hunting after a weak stretch lifted U.S. stocks. Treasury debt prices fell, losing some of their safe-haven appeal. The dollar was little changed against a basket of currencies.
Following on the heels of April's sluggish employment gains, the claims data calmed fears the labor market was stagnating. Companies added a meager 115,000 new jobs to their payrolls in April, the fewest in six months, the government said on Friday.
Most economists have viewed the pull-back in job creation as payback for stronger activity during the unusually warm winter and believe the underlying pace of payrolls growth is around 175,000 a month - its average for the past three months.
Scott Brown, chief economist at Raymond James in St. Petersburg, Florida, said the jobless claims figures had "simmered down after the noises we had earlier."
"This shows we have moderate job growth. They're consistent with monthly job payroll growing at 150,000 to 180,000," he said.
Other data showed no sign of inflation pressures, with retreating crude oil prices pushing down the cost of imported goods in April by the most in 10 months.
That should help to lower the cost of living for many households and support economic growth.
"With external demand, particularly in Europe and oil prices having eased ... import price pressures are likely to remain subdued in the coming months," said Peter Newland, an economist at Barclays in New York.