The government revised its estimate of economic growth during the second quarter to a 3.1 percent annual rate, a considerable improvement over the government’s initial second-quarter estimate of 2.4 percent issued just a month ago.

The size of the revision exceeded the expectations of private economists. The latest estimate is more than double the 1.4 percent rate recorded during the two previous quarters.

“The future is looking a little brighter than it was before,” said senior economist Ken Matheny of Macroeconomic Advisers in St. Louis. “It’s almost a dead cinch that we’re going to have pretty healthy gains in the third quarter.”

But the second-quarter gain was not necessarily stout enough to cause an improvement in the flagging job market. The Labor Department reported that initial claims for unemployment benefits rose 3,000 to a seasonally adjusted 394,000 last week, suggesting that the gains of recent months have not yet prompted many employers to increase their work forces.

“This is not just a jobless recovery, it has been almost a job-shedding recovery,” said economist Jay Feldman at Credit Suisse First Boston.

Even President Bush acknowledged that unemployment remains stubbornly high.

“The president is pleased to see that the recovery appears to be taking hold,” said White House spokesman Claire Buchan. “But he isn’t satisfied. And he won’t be satisfied until every American who wants to find a job can do so.”