California, which is still dealing with technical problems from the upgrading of its computers, accounted for about half of the increase in claims, a Labor Department analyst said.
Troubles converting to the new system had resulted in a backlog of claims, which were now being pushed through, he said.
In addition, 15,000 of the claims were from nonfederal workers affected by the partial government shutdown, which is now in a second week, the analyst said.
Economists polled by Reuters had expected first-time applications to rise to 310,000 last week.
The four-week moving average for new claims, which irons out week-to-week volatility, increased 20,000 to 325,000.
Claims data are collected by states, and weekly jobless is the only government report being published during the shutdown.
In the absence of the comprehensive employment report for September, whose publication has been delayed indefinitely, the claims report is being closely watched for clues on the health of the job market.
The claims report showed the number of people still receiving benefits under regular state programs after an initial week of aid fell 16,000 to 2.91 million in the week ended Sept.28.