Claims for new jobless benefits in the U.S. are continuing to fall, the latest sign of an improving labor market in the world’s largest economy.

The government said Thursday that 351,000 workers made initial claims for unemployment compensation last week, 2,000 fewer than the week before. Claims for jobless assistance in the U.S. have generally been falling since mid-2011.

The weekly total is now at a level last seen nearly four years ago, just before the start of the country’s worst economic downturn since the Great Depression in the 1930s.

The four-week average of new claims has dipped to 354,000, somewhat below the 375,000 figure that economists say would indicate a healthy labor market. When companies lay off fewer workers, it usually indicates that some employers are also starting to hire more employees.

Even so, about 13 million U.S. workers remain unemployed, many of them for extended periods of time. While the country’s jobless rate fell to 8.3 percent in January, that is still an elevated figure by U.S. standards.

The chairman of the U.S. central bank, Ben Bernanke, told a congressional committee Thursday that he worries that more than 40 percent of jobless workers in the U.S. — about 5.5 million — have now been unemployed for more than six months. He said that as workers remain unemployed for extended periods, they run the risk of losing their job skills and could have trouble regaining them.

He said the country’s job market is “far from normal” and described the rate of growth of the country’s economy as “modest.” The U.S. economy advanced at an annual rate of 3 percent in the last quarter of 2011, but government analysts are predicting lower growth this year of 2.25 percent.