The Labor Department says the four-week average, a less volatile measure, fell for the third straight week to 331,500. Both figures are close to pre-recession levels and suggest that companies are laying off few workers.
Still, hiring will also need to pick up to make a dent in the still-high 6.7 percent unemployment rate. Many economists forecast that job gains will pick up a bit this year.
"An array of surveys tell us labor demand is rising, and we remain of the view that the underlying trend in payroll growth is slowly picking up," said Ian Shepherdson, an economist at Pantheon Macroeconomics.
One sour note in the report: Nearly 1.4 million people who have been unemployed longer than six months lost benefits in the week that ended Jan. 4, the latest period for which figures are available. That's because an emergency program that provided extended benefits expired Dec. 28.
The number of recipients fell to 3.7 million from 4.7 million in the previous week. About 300,000 people began receiving unemployment benefits in the week ended Jan. 4.
The total number of beneficiaries was already declining as those out of work either found jobs or exhausted their benefits. More than 5.6 million people were receiving aid a year ago. The program peaked with just over 11 million recipients in early 2010, about six months after the Great Recession ended.
The figures show that only about one-third of those out of work now receive aid. That's low by historical standards. The figure is usually closer to half.
More than 10 million people were unemployed in December. Benefits are available only to those who lose their jobs through no fault of their own. Those who quit or were fired for performance reasons or who have started looking for work after finishing school don't qualify for benefits.
President Barack Obama and congressional Democrats pushed to extend the emergency program for another three months. But they couldn't reach agreement with Republicans, who wanted to cut spending to offset the $6 billion estimated cost. The extended benefits had been available since 2008.
The program provided up to 47 extra weeks of aid, paid for by the federal government. It offered payments averaging $256 a week to people who had exhausted their state benefits, which typically last for six months.
Economists predict that the expired benefits will cause the unemployment rate to fall by as much as a quarter of percentage point in early 2014. The decrease will likely happen because many of the former recipients will give up on their job searches, which are required in order to receive benefits.
As a result, they will no longer be counted as unemployed. The government counts people as unemployed only if they are looking for work.
The unemployment rate fell last month to 6.7 percent from 7 percent. Much that decrease came from 347,000 unemployed workers leaving the workforce. A mere 74,000 jobs were created in December, after average monthly gains of 214,000 new jobs in the previous four months.
There are signs that economic growth is accelerating. Consumer confidence and retail spending have picked up in the October-December quarter. Orders to U.S. manufacturers rose in November, a sign that businesses are investing more on factory-made items such as machinery, computers and electrical goods. Factory output rose for a fifth straight month in December.
The economy is still far from healthy. Income rose at a slower pace than spending last month, which means Americans are spending more but saving less. And sales of existing homes have dropped for three straight months, held back by higher prices and mortgage rates.
Still, many economists have become more optimistic about the October-December quarter. Several are predicting a solid annual growth rate of 3 percent or more. That's up from estimates a month ago of as low as 1.5 percent.