Economists argue that the labor market is healthier when applications fall below 375,000, reflecting a slower pace of layoffs.
Job growth in March slowed to 88,000 arousing new concern about the condition of the economic recovery.
Businesses have said that uncertainty about policy directions in Washington are holding them back from picking up hiring that would significantly lower the unemployment rate.
The jobless rate dropped to 7.6 percent in March from 7.7 percent but that was mostly because people stopped looking for work.
The first estimate of gross domestic product is due out Friday morning and economists expect that growth through the first three months of the year picked up pace to possibly 3 percent, which would be much faster than the 0.4 percent in the final quarter of 2012.
Despite the expected improvement, growth could slow into the summer with billions in automatic spending cuts expected to weigh on the recovery, economists have said.