A department spokesman said Hurricane Sandy had no effect on the number of applicants. The report covered the week ending Oct. 27, before the storm reached shore.
But the devastation and economic disruptions that the storm caused this week will likely increase applications for unemployment aid in coming weeks. Workers who have been temporarily laid off because of the storm are expected to seek benefits.
Applications have fluctuated between 360,000 and 390,000 since January. During that time, employers have added an average of about 150,000 jobs a month. That's reduced the unemployment rate from 8.3 percent in January to 7.8 percent in September.
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.
Still, the economy is growing too slowly to rapidly bring relief to roughly 12 million out-of-work Americans. With the unemployment rate still high, steady growth of more than 3 percent is generally needed to create a sufficient number of jobs.
The unemployment rate fell to 7.8 percent in September. That's the first time the rate has been below 8 percent since January 2009, President Barack Obama's first month in office.
The rate fell because a government survey of households found a huge increase in the number of people who had jobs. Still, a jump in part-time employment accounted for most of the gain.