The four-week average of applications, a less volatile measure, rose slightly to 365,500, the Labor Department said Thursday. That is still a level consistent with modest hiring.
Last week, California reported a large drop in applications, pushing down the overall figure to the lowest since February 2008. This week, it reported a significant increase. The gyrations occurred because it processed applications last week that were delayed from the previous week.
A department spokesman said the seasonally adjusted numbers "are being distorted ... by an issue of timing."
Applications are a proxy for layoffs. When they consistently fall below 375,000, it suggests hiring is healthy enough to lower the unemployment rate.
Several economists simply calculated the average of the two distorted weeks, which is 365,000. That's in line with the recent trend. But it's modestly improved from September, suggesting that hiring could be a bit better this month.
"Though still struggling, the U.S. labor market appears to be making headway, and we should see a modest improvement in October ... payrolls," Sal Guatieri, an economist at BMO Capital Markets, said in an email to clients.
The number of people receiving benefits fell. Just over 5 million people received unemployment aid in the week ending Sept. 29, the latest data available. That was about 40,000 fewer than the previous week.
Some recent reports suggest the economy is picking up. Retail sales grew in September at a healthy clip. And builders started construction on new homes and apartments last month at the fastest pace in more than four years.
Still, the economy is not growing fast enough to generate much hiring. Growth slowed to a tepid annual rate of 1.3 percent in the April-June quarter, down from 2 percent in the previous quarter. Most economists see growth staying at or below 2 percent in the second half of the year.
The unemployment rate fell in September to 7.8 percent, the lowest level since January 2009, the department said earlier this month. It fell because a government survey of households found a huge increase in the number of people who had jobs. A jump in part-time employment accounted for most of the gain.
Employers, meanwhile, added 114,000 jobs in September, according to a separate survey of businesses. Hiring in July and August was also revised much higher.
As a result, the economy gained an average of 146,000 jobs a month in the July-September quarter. That's more than double the monthly pace in the April-June quarter.
Even so, hiring must be stronger to bring relief to the more than 12 million people who are unemployed. Roughly 100,000 new jobs are needed each month just to keep up with the working-age population.