The Labor Department said Thursday that the less volatile four-week average fell for the third straight week to 338,500. Both figures are near pre-recession levels.
Applications are a proxy for layoffs. They had spiked in early October because of the partial government shutdown and processing backlogs in California. But first-time applications have now fallen in five of the past six weeks. The decline indicates that employers are laying off fewer workers.
"If claims can remain at this week's level it would be easier to believe in the idea that ... payroll growth could break out to the upside," said Ian Shepherdson, chief economist at Pantheon Macroeconomics.
Some economists warned that last week's Veterans' Day holiday may have exaggerated last week's decline because many state government offices were closed on Nov. 11.
But the broader trend has been downward. The steady declines suggest hiring will remain healthy in the coming months. Employers added 204,000 jobs in October, shrugging off the 16-day shutdown.
Job growth accelerated over the summer. Employers added an average of 202,000 jobs per month from August through October. That's up sharply from an average of 146,000 in May through July.
The solid gains should help boost economic growth next year. Greater hiring, combined with modest increases in pay, appears to be supporting more spending. Higher retail spending last month has raised hopes that the holiday shopping season will be better than many analysts expected.
Still, the economy is far from healthy. More than four years after the recession officially ended, the unemployment rate remains high at 7.3 percent.
And nearly 3.9 million people received benefits during the week ended Nov. 2, the latest data available. That's down about 33,000 from the previous week. That total has fallen 26 percent in the past year. Many of the former recipients have likely found jobs. But most have likely used up all the benefits available to them
The Federal Reserve is closely monitoring the job market in deciding when to reduce its economic stimulus. The Fed has been buying bonds to keep long-term interest rates low and encourage more borrowing and spending.