The US Defence Secretary, Donald Rumsfeld, has acknowledged the need for more forces to improve security in Iraq, but says they should be provided by other countries or from the Iraqis themselves, not the US.
The US wants more troops in Iraq as long as they are not American
Mr Rumsfeld was speaking as he began an unannounced trip to the Gulf region, where he is expected to meet senior American commanders overseeing the US military effort in both Iraq and Afghanistan.
Mr Rumsfeld said he would like to see another 10,000 foreign troops in Iraq - and added that it was critical to get more local forces to bolster the 50,000 Iraqi personnel already in place.
His visit comes as the Bush administration is trying to get a mandate from the United Nations for an international force in Iraq.
It hopes this would secure contributions from countries such as India and Pakistan, who have been unwilling to join the present US-led coalition.
Mr Rumsfeld said he accepted that nations which provided help should be allowed to have a say in Iraq's future.
The US is also hoping to get more countries to share the burden of reconstruction, observers say.
The BBC's Justin Webb in Washington says the US will stress the role of the Iraqi institution it has set up in the UN draft resolution.
The White House hopes that the Iraqi Governing Council will be fully endorsed by the UN, our correspondent says.
The council might then issue requests for troops and money - which Islamic nations in particular could respond to while distancing themselves from America and the original decision to go to war.
Under the resolution, US commanders would remain in
charge of peacekeeping operations in Iraq, but there, too, "We are asking the international community to join us even more than they have in the past," US Secretary of State Colin Powell said.
The resolution may be ready for submission to the Security Council next week, he said.