However, Prime Minister Ibrahim al-Jaafari warned against setting a timetable for foreign troops to leave "at a time when we are not ready" to confront "the insurgents".
But he said security in many of Iraq's 18 provinces - notably in the Shia south and the Kurdish-controlled north - has improved so that Iraqi forces could assume the burden of maintaining order in cities there.
"We can begin with the process of withdrawing multinational forces from these cities to outside the city as a first step that encourages setting a timetable for the withdrawal process," al-Jaafari said at a news conference with US Deputy Secretary of State Robert Zoellick.
"We don't want to be surprised by a decision to withdraw at a time when we are not ready," he said.
Al-Jaafari's comments were aimed partly at defusing growing calls by Sunni Arabs and others for the Americans to set a date to leave Iraq.
The prime minister, a Shia, told parliament on Tuesday that he wanted any withdrawal plan to be "an Iraqi decision with an Iraqi timetable - not with a terror timetable".
He did not specify which cities could be turned over to the Iraqi security forces. The uprising is focused in Baghdad and the Sunni Arab heartland of central and northern Iraq. Wide areas of the Shia south and Kurdish north have been relatively peaceful.
Most US troops are based in areas
which are home to armed fighters
Most of the 135,000 American soldiers are based in areas which are home to armed fighters and deemed too dangerous to hand over to Iraqi forces soon.
Zoellick said Washington was committed to supporting the new Iraqi leadership and that US troop strength "will be based on the conditions by which the Iraqi forces are able to meet the effort to deal with the counterinsurgency".
However, the Defence Department wants to pull some troops out of Iraq next year, partly because the commitment is stretching the army and Marine Corps perilously thin as casualties mount. US commanders believe the presence of a large US force is generating tacit support for anti-American attacks.
Last weekend, the British newspaper The Mail on Sunday published a leaked British government memorandum showing that Britain is considering scaling back its forces from 8500 to 3000 by the middle of next year.
The memo, marked Secret - UK Eyes Only and signed by Britain's Defence Secretary John Reid, also spoke of a "strong US military desire for significant force reductions" after a new Iraqi government is elected in December.
Iraqi police perform a drill in Hilla,
where Zoellick visited on Tuesday
"Emerging US plans assume that 14 out of 18 provinces could be handed over to Iraqi control by early 2006," which would see the multinational force cut from 176,000 to 66,000, the memo said.
British officials said the document was authentic, but merely reflects the government's long-standing plan to train Iraqi forces and gradually hand over security responsibility.
Zoellick's visit came one day after he signed four economic agreements with Iraqi officials in neighbouring Jordan. He travelled later to Hilla, 96km south of Baghdad, to watch US-led soldiers train Iraqi police and to discuss reconstruction plans with local officials.