Passage of the emergency spending legislation capped a four-month struggle between Bush and a new Democratic-controlled congress determined to force him to shift course in the unpopular war.
Bush had vetoed an earlier bill that would have required him to begin withdrawing soldiers from Iraq by October 1, and he had vowed to kill any legislation carrying restrictions on troop deployments.
"Let the people of Iraq vote if they want the US to stay or leave"
Bob Kaye, Bohemia, US
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With Democrats lacking the votes to override the president and the war funds running out, a divided Congress passed a compromise measure on Thursday.
"We've got a good bill that doesn't have timetables or tell the military how to do its job but also sent a clear signal to the Iraqis that there's expectations here in America .... about how to move forward," Bush said after visiting wounded military personnel at a naval hospital in Bethesda, Maryland.
Bush has made clear that September will be an important period, when General David Petraeus, the US commander in Iraq, will report on the impact of the troop build-up and make a recommendation on how to proceed.
The legislation gives Bush the funds he sought without any requirement that he bring troops home, but it does set a series of "benchmarks" for the Iraqi government to meet and ties a small amount of non-military US aid to achieving progress.
Despite losing the latest round to Bush, Democrats vowed to keep up their efforts to force him to start bringing US troops home from Iraq.
Criticised by US anti-war groups for allowing the bill to pass, Nancy Pelosi, the House of Representatives speaker, said Democrats would quickly resume their drive to impose deadlines for pulling US forces out of Iraq.
She said she would put on the house agenda a bill to repeal Congress' 2002 authorisation of the Iraq war and said Democrats would use next year's military spending bills to try to end the war that has killed at least 3,420 US soldiers and wounded more than 34,000.
Iraqis have suffered far worse casualties.