New U.S. claims for jobless benefits fell last week to their lowest level since early April and the trade deficit unexpectedly shrank in September, pointing to a slight improvement in the sluggish economy.

The Labor Department said on Thursday that initial claims for state unemployment benefits fell for the second straight week, dropping 10,000 to a seasonally adjusted 390,000.

That is still well above levels seen before the 2007-2009 recession, but below a 400,000 claims level which economists say could likely prompt some acceleration in hiring.

Clearly, the labor market is improving, but at a very slow pace, said Omer Esiner, chief market strategist at Commonwealth Foreign Exchange in Washington.

In a separate report, the Commerce Department said the U.S. trade deficit shrank 4 percent to $43.1 billion in September.

The gap was the narrowest since December thanks to record-high exports, and suggested the U.S. economy closed the third quarter a little stronger than previously believed.

The government could raise its estimate for third quarter growth to a 2.8 percent annual rate from 2.5 percent, said Paul Dales, an economist at Capital Economics in Toronto.

Still, economists say the economy must grow much faster to put a big dent in the jobless rate, which has been stuck at or above 9 percent for most of the last two years.

(The data) are not strong enough to make it clear that we are in a solid recovery but they are not weak enough to show that we are falling into a recession, said Rick Meckler, president of investment firm LibertyView Capital Management in New York.

While companies are cutting back on layoffs, they aren't stepping up hiring much. Nonfarm payrolls rose a tepid 80,000 last month, the government said last week.

Prices for U.S. government debt extended losses on the claims and trade data, although traders were more focused on Europe's unfurling debt crisis, which threatens the global economy. U.S. stocks gained.

CHINESE IMPORTS

The trade report also showed a narrowing of the politically sensitive deficit with China. China has allowed its yuan currency to appreciate 4.3 percent over the last year as the Asian giant tries to rebalance its economy toward domestic consumption and depend less on exports.

The U.S. data showed Chinese imports fell 2.5 percent in September. A report in Beijing showed the country's imports surged in October as exports grew at their slowest rate in months.

Still, the United States and other countries are pressing China to let the yuan strengthen more, and many of the Republican candidates eyeing the White House have vowed to turn up the heat on China.

A separate report showing a 0.6 percent fall in import prices during October also painted a bright spot for the economy.

Americans' wages have not kept up with high inflation in recent months, making it harder for consumers to step up spending and power the economy. Many analysts, however, think inflation may have peaked.

(Additional reporting by Lisa Lambert in Washington and by Steven C. Johnson and Angela Moon in New York; Editing by Chizu Nomiyama; Editing by Andrew Hay)