The Labor Department says the four-week average of applications, a less volatile figure, fell 3,500 to 327,00, the lowest since late November.
Applications are a rough proxy for layoffs. Their current pace suggests that companies are confident enough about economic growth to keep their staffs.
Hiring picked up in February after brutal winter weather slowed job growth the previous two months. Employers added 175,000 jobs last month, up from just 129,000 in January and only 84,000 in December.
About 3.35 million people received unemployment benefits as of March 1, the latest figures available. That's about 101,000 fewer than the previous week.