Still, a four-week average of new claims, which smooths out volatility, fell 5,250 from a week earlier.
The data reinforces the view that the labor market is weathering this year's tax hikes and federal budget cuts, which appeared to drag heavily on economic growth during the first half of the year.
Indeed, Thursday's claims data was drawn from the same survey week in which the Labor Department polls employers to estimate how many jobs the economy added during the full month.
Compared to the same survey week in June, the four-week average was 0.7 percent lower last week.
A Labor Department analyst said there was nothing unusual in the data and that no states had provided estimates.
Economists polled by Reuters had expected first-time applications to fall to 345,000 last week. Claims for the prior week were revised to show 2,000 fewer applications received than previously reported.
The U.S. labor market has shown signs of strength in recent weeks, with 195,000 jobs added to payrolls in June. This has fueled expectations the Federal Reserve will start winding down its massive stimulus program as early as September.
At the same time, Fed Chairman Ben Bernanke said this week the Fed would only begin withdrawing its support if the economy improves as much as policymakers expect.
The claims report showed the number of people still receiving benefits under regular state programs after an initial week of aid rose 91,000 to 3.1 million in the week ended July 6.