The Labor Department said Thursday that the four-week average of applications, a less volatile measure, rose by 3,250 to 370,500.
The storm could affect weekly applications for up to four weeks, a Labor spokesman said.
Applications declined in one state last week because power outages prevented officials from receiving applications. The spokesman wouldn't identify the state. The storm also pushed applications in other states up because some people who could not go to work sought benefits.
Most economists expect applications will rise in the coming weeks. Jill Brown, an economist at Credit Suisse, said that large hurricanes have historically pushed up applications by about 4 percent. That suggests they could reach 390,000.
If applications stay below 360,000 after the storm's effects fade, it would be a good sign for the job market.
Weekly applications have fluctuated between 360,000 and 390,000 since January. At the same time, employers have added an average of nearly 157,000 jobs a month. That's only been enough to lower the unemployment rate slowly. It has declined to 7.9 percent from 8.3 percent this year. And some of the decline was because more people gave up looking for work and weren't counted as unemployed.
The number of people receiving benefits rose to nearly 5.1 million in the week ended Oct. 20, the latest data available. That's about 42,000 more than the previous week.
There are some signals that the job market is improving. Employers added 171,000 jobs in October and hiring in August and September was much stronger than first estimated, the department said last week. The economy has gained an average of 173,000 jobs a month since July. That's up from 67,000 a month in April through June.
The unemployment rate rose to 7.9 percent in October from 7.8 percent in the previous month. But that is because more Americans began looking for work, possibly because they felt their chances had improved. Not all of them found jobs, which pushed up the unemployment rate.
Employers posted fewer available jobs in September than in August, according to a separate report from the Labor Department on Tuesday. That happened after job openings were revised higher in August. Employers filled fewer openings, the report showed, but layoffs also fell.
The economy picked up slightly this summer after a sluggish spring. Growth rose to a 2 percent annual rate in the July-September quarter, up from 1.3 percent in the April-June quarter. Consumers and the federal government spent more, and the housing market contributed to growth for the sixth straight quarter.
Most economists expect growth will remain sluggish through early next year. Many hope the economy will accelerate if the White House and Congress avoid the so-called "fiscal cliff," the package of tax increases and spending cuts scheduled to take effect early next year. If the cliff isn't avoided, it could push the U.S. economy back into recession.
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