The Labor Department says the four-week average, a less volatile measure, increased 6,750 to 347,250, the third straight gain. The average had fallen to a five-year low of 338,000 earlier this month.
Weekly applications are a proxy for layoffs. They have been at about 350,000 or below for most of this year. At the same time, hiring has been solid. In the past six months, employers have added an average of 208,000 jobs per 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 percent, down from 10 percent in October 2009. Some of the decrease is because many people have given up looking for work. The government counts people as unemployed only if they are actively searching for a job.
Two reports this week suggested that the economy is still expanding modestly, despite an increase in Social Security taxes at the beginning of the year and federal government spending cuts that kicked in March 1.
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 percent 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. 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.