Fewer Americans filed applications for unemployment benefits last week, a sign the labor market is improving heading into the second quarter, Bloomberg reported.

U.S. Department of Labor numbers showed that claims fell by 6,000 to 388,000 in the week ended March 26.

A slowdown in firings and growing payrolls may bolster further gains in consumer spending, as companies added 210,000 jobs in March and unemployment remained at 8.9 percent, according to projections of a Labor Department report that will be released tomorrow.

“The labor market is slowly but surely improving,” said Ryan Sweet, a senior economist at Moody’s Analytics Inc. in West Chester, Pa., in an interview with Bloomberg. “We’ll see hiring begin to accelerate over the next couple months.”

The number of people continuing to receive unemployment benefits dropped by 51,000 in the week ended March 19 to 3.71 million, the fewest since October 2008.