* Weekly jobless claims fall 4,000
* Continuing claims unexpectedly rise
* Import prices rise on energy, ex-petroleum gain modestly
WASHINGTON, May 13 (Reuters) - The number of U.S. workers filing for jobless benefits fell only slightly last week, highlighting the challenges facing the labor market, while import prices pointed to tame inflation, according to government data released on Thursday.
Initial claims for state unemployment benefits slipped 4,000 to a seasonally adjusted 444,000, the Labor Department said, though the number was still slightly above the 440,000 expected by analysts in a Reuters poll. The prior week's figure was revised up to 448,000.
In a second report, the department said import prices increased 0.9 percent last month on higher petroleum costs after rising 0.5 percent in March. However, excluding the volatile petroleum category, import prices rose just modestly.
Analysts said the slow decline in jobless claims against the backdrop of a pickup in the pace of job growth was puzzling, saying it pointed to a high unemployment rate.
"There are more jobs being created, but the general trend is that businesses are still reluctant to hire. The data show that the issue is more a lack of hiring and not people getting laid off," said Gary Shilling, president at A. Gary Shilling & Co in Springfield, New Jersey.
"That's why the unemployment rate remains where it is."
The jobless rate is currently at 9.9 percent.
U.S. stock futures trimmed gains on the data, while Treasury debt prices edged up slightly. The U.S. dollar extended gains versus the euro.
Though initial jobless claims are decreasing only slowly, other measures of the labor market -- including the government's closely watched employment report -- suggest job growth is gaining traction as private sector employers become more confident of the strength of the economic recovery.
Payrolls grew at the fastest pace in four years in April, according to government data last week that also showed the fourth straight month of gains in employment. The economy has grown for three straight quarters following the worst recession since the 1930s.
However, challenges remain in the job market. The number of people still receiving jobless benefits after an initial week of aid unexpectedly rose 12,000 to 4.63 million in the week ended May 1, the Labor Department said.
The level was well above market expectations for 4.58 million. The insured unemployment rate, which measures the percentage of the insured labor force that is jobless, was unchanged at 3.6 percent for a fourth straight week.
With unemployment still at elevated levels and inflation pressures remaining relatively benign, the Federal Reserve should be able to keep its promise of ultra low interest rates for an extended period.
Import prices excluding petroleum rose 0.3 percent after slipping 0.1 percent in March.
Analysts generally expect U.S. dollar strength and excess capacity in the global economy to keep a lid on prices of imported merchandise, excluding petroleum.
The Labor Department report also showed export prices rose 1.2 percent in April, building on the prior month's 0.7 percent advance. Analysts had expected export prices to gain 0.4 percent. In the 12 months to April, export prices increased 5.7 percent, the largest gain since July 2008. (Reporting by Lucia Mutikani; Editing by Chizu Nomiyama)