The Labor Department says the four-week average, a less volatile measure, inched up 6,750 to 347,250, a third straight increase.
Weekly applications are a proxy for layoffs. Earlier this month, they fell to 338,000, the fewest in any week since 2008.
The decline in applications for unemployment aid has coincided with solid hiring. In the past six months, employers have added an average of 208,000 jobs a month. That's up from an average of only 138,000 in the previous six months.
The unemployment rate has fallen to a four-year low of 7.5 per cent, down from 10 per cent in October 2009. The drop in unemployment has occurred, in part, because many people have given up looking for work. The government counts people as unemployed only if they are actively searching for a job.
"We can't make too many inferences from one week's results but the trend, overall, still points to improving labour markets," said Jennifer Lee, an economist at BMO Capital Markets.
Five states were unable to report complete data to the Labor Department, a spokesman said, because of the Memorial Day holiday earlier this week. The department estimated figures for those five states. That could mean that last week's figure will be revised more than usual next week when the final data is received.
Nearly 4.6 million Americans were receiving unemployment benefits the week that ended May 11, the latest data available. That's down 25 per cent from 6.1 million a year earlier.
A separate report Thursday showed that the economy expanded at a 2.4 per cent annual pace in the first three months of the year. That was slightly below an earlier estimate of 2.5 per cent but much better than the 0.4 per cent pace in the final three months of last year.
Economists expect growth will slow to about 2 per cent in the current quarter, as businesses and consumers adjust to tax increases that took effect at the beginning of the year and federal government spending cuts that kicked in March 1.
Two reports this week suggested that the economy is still expanding at a steady pace. Home prices are surging and consumers are more confident. Both trends could encourage more spending in the coming months, providing crucial support for growth.
Consumer confidence jumped in May to the highest level in five years, the Conference Board said Tuesday. Soaring stock prices and Americans' brighter outlook on the job market helped drive the gain.
Home prices jumped nearly 11 per cent in March from a year earlier, according to the Standard & Poor's/Case-Shiller home price index, also released Tuesday. That is the biggest gain in seven years.
Higher prices increase homeowners' net worth, which makes them more likely to spend. They can also sustain the housing recovery, by encouraging more would-be buyers to purchase homes before prices rise further.
More buyers are bidding on a tight supply of homes. That's encouraged builders to step up construction, which creates more jobs. Applications for building permits rose to the highest level in five years in April.
The brightening economic picture has raised speculation that the Federal Reserve would dial back its $85 billion a month bond-buying program. The purchases are intended to lower long-term interest rates and encourage more borrowing and spending.
Fed Chairman Ben Bernanke told Congress last week that it was too early to wind down the program. Fed policymakers have said they will continue the purchases until there is substantial improvement in employment.