By DPA
Bush referred to the dispute in a statement late Friday saying: "Rather than mandate arbitrary timetables for troop withdrawals or micromanage our military commanders, this legislation enables our servicemen and women to follow the judgement of commanders on the ground."
Bush vetoed an earlier version that contained firm deadlines for withdrawal by 2008.
The law passed after the centre-left Democrats now in control of both houses of Congress failed to muster the necessary two-thirds majorities to override a presidential veto.
The compromise legislation comes after weeks of negotiations between the opposition Democrats and the White House as funding for the US military presence in Iraq began to dwindle during an ongoing surge of 20,000 US troops ordered by Bush in January.
Many Democrats said they voted against the bill because it did not go far enough to begin planning for the departure of US troops from the Iraq conflict, which began with an invasion ordered by Bush in March 2003.
As part of the compromise, Bush supported a Republican proposal that includes 18 benchmarks that the Iraqi government must meet or risk losing financial support. Some Democrats argue the benchmarks are too weak and difficult to enforce.
Senators Hillary Rodham Clinton of New York and Barack Obama of Illinois, both top candidates for the Democratic Party's 2008 presidential nomination, voted against the measure without deadlines.
Clinton, who voted in 2002 to authorize military action in Iraq, has struggled to placate the left wing of her party, which still resents her early support for what they see as Bush's war.
"The anti-war movement will not be silenced by this setback – we will continue to organize and make our voices heard," said Judith Le Blanc, co-chairwoman of United for Peace and Justice, an anti-war coalition.
"This Congress has the power to end the war, and they must find the political will to accomplish what they were elected to do."