377 Representatives voted in favor of it and requiring President Bush to report to Congress in 60 days, and every 90 days thereafter, on the status of its redeployment plans in Iraq.
The Democratic-led House has passed a sheaf of bills calling for a pullback from Iraq, but without the two-thirds majority required to override a presidential veto.
As the first compromise made on the Democrats-proposed bill concerning the war policy, Republicans said they agreed to back it up because it encourages Pentagon contingency planning already under way and does not mandate troop withdrawals.
"If this war is important enough to fight, then it ought to be important enough to pay for," said David Obey, chairman of the House Appropriations Committee who sponsored the plan.
"By putting together this bill we hope people will stop ignoring what this war is costing American taxpayers and call the president's bluff on fiscal responsibility," he said.
The tax plan requires low- and middle-income taxpayers to add 2 percent and wealthier people add a 12 to 15 percent to their tax bill, which incurred opposition from Democrat House Speaker Nancy Pelosi and Republican congressmen.
"Just as I have opposed the war from the outset... I am opposed to a war surtax," she said.
The war in Iraq is costing the United States about 10 billion dollars a month, while Afghanistan and other missions run about 2 billion dollars a month, according to official statistics.