Iraq's vice-president has warned that a quick withdrawal of US troops could worsen the security situation in Iraq.
Some Democrats want US troops to be brought home now
Tareq al-Hashemi responded after the US House of Representatives passed a bill imposing a deadline for all US troops to leave Iraq by 31 August 2008.
Mr Hashemi said replacing US troops with poorly-trained Iraqis whose loyalty was questionable would create a security vacuum.
US President George W Bush vowed to veto the Democratic-sponsored bill.
"I do believe that for the common interest of my country we need coalition forces to stay until further notice," Mr Hashemi said on a visit to Japan.
"We are expecting a timetable for conditional withdrawal," he said, adding that was in the national interest of Iraq, the US and the UK.
Speaking after the vote, Mr Bush described the legislation as an "abdication of responsibility".
The bill was passed by 218 votes to 212 by the Democratic-controlled House. Correspondents say it is the biggest challenge yet to Mr Bush's war policy.
But while much of the debate centred on Iraq, Republicans were critical of millions of dollars worth of subsidies tagged onto the bill in what they said was an effort to win votes from hesitant Democrats.
A grim-faced President Bush said the vote, which was largely along partisan lines, was an effort to "force me to accept restrictions on our commanders, an artificial timetable for withdrawal and their pet spending projects".
"This is not going to happen," he said.
The White House says legislators should allow more time for Mr Bush's "surge" strategy - which includes sending 28,000 extra troops to Iraq - to work.
The Senate is expected to vote next week on legislation similar to the House bill.
To pass the Senate version, the Democrats would need the support of about a dozen Republican senators.
The House vote was a victory for the Democratic leader, Nancy Pelosi.
She said Congress had "voted no to giving a blank cheque to an open-ended commitment to war" and "yes to begin the end of the war and the redeployment of our troops".
The bill was primarily to authorise $124bn (£62bn) in funding for US troops in Iraq and Afghanistan.
Some Democratic representatives voted against it, because they want to put an immediate end to the war.
Others opposed it because it could make the work of military commanders more difficult.
Most Republicans opposed the legislation, which they said would represent an admission of failure in Iraq.
"The stakes in Iraq are too high and the sacrifices made by our military personnel and their families too great to be content with anything but success," Republican Roy Blunt said.
The House bill calls for the withdrawal of troops to begin as early as July 2007 if there is no evidence progress is being made in bringing order to Iraq.