BBC News Online looks at key members of the US-led coalition in Iraq and countries which might be likely to contribute troops to a UN-approved multinational force for Iraq if the United States and the Security Council can agree a new resolution on the occupation.
Click on the countries below to see where they stand.
At the UN, the United States is pushing for a new resolution that will allow countries to sign up to a multinational force.
Several council members are reluctant to approve a resolution that gives retroactive blessing to the Iraq war, which they refused to back. They have also insisted that any new resolution give genuine power to the UN rather being a fig leaf for a US-run occupation.
It appears that France, Russia and China are unlikely to veto the US-proposed resolution because they want to avoid another bruising confrontation. However, unless they actually vote for the resolution, it may not be perceived as having the international backing that would bring countries such as India and Turkey on board.
China, Russia and France have indicated that they back proposals to reduce the political role of the US and UK in Iraq.
The US has an estimated 140,000 troops in Iraq. Its forces are taking almost daily casualties, and the operations and the early reconstruction effort are costing Washington dearly - President Bush has turned to Congress for a further $87bn for military operations in Iraq and Afghanistan.
Politically the deaths of US servicemen and the cost of the war could be very damaging to President Bush.
With an eye on re-election next November, he is turning to other states and the UN in the hope that they will shoulder some of the financial burden and to put troops on the ground in Iraq.
The UK has at least 10,000 soldiers in Iraq and is sending about 1,200 more. UK forces control the southern region of Iraq where the lack of security is not as severe as in Baghdad and to the north of the capital.
UK officials have said their troop commitments to Iraq are long term. Prime Minster Tony Blair strongly supports an increased UK role in Iraqi reconstruction and peacekeeping.
Polish soldiers are commanding a 9,000-strong multinational force in the south-central region of Iraq.
Poland, along with most of the former communist countries of central Europe and the Balkans was a firm supporter of the US-led attack on Saddam Hussein's Iraq. And alone among continental European countries, Poland sent a small military contingent to fight there during the war.
More than 2,000 Australian troops fought alongside American and British troops in the campaign. The Canberra government is facing a congressional inquiry into the intelligence that led it to send troops to Iraq and allegations that it exaggerated the threat posed by Iraqi weapons of mass destruction.
Prime Minister John Howard said his country would not be sending peacekeepers to Iraq, even if the UN backed the idea of a multinational force.
France is insisting on a central role for the UN which goes beyond the limited one offered in Security Council resolution 1483, under which the UN is subsidiary to the occupying powers. It is also arguing for a political approach.
"The only realistic option is to transfer authority and sovereignty to the Iraqis themselves. This must be done rapidly as part of a process which only the United Nations can render fully legitimate," Roland Galharague of the French embassy in London told BBC News Online.
"For our country, whatever measures may ultimately be adopted cannot simply be an enlargement or adjustment of the present occupying forces."
Germany - which has 10,000 troops committed in peacekeeping operations around the world - says it "does not have the capacity" to contribute to a multinational force for Iraq. Germany intends to expand its peacekeeping operations in Afghanistan, where it already has 1,800 troops.
Russia "does not rule out" sending peacekeepers to Iraq if an appropriate UN Security Council resolution is passed. Defence Minister Sergei Ivanov said that everything depended on how far the Security Council would be given a real opportunity to influence the development of the situation in the country.
On 7 October, the Turkish parliament approved a government motion allowing troops to be sent to Iraq. However shortly before the vote, some members of the US-appointed Governing Council in Baghdad said they would not accept troops from any neighbouring state on its soil.
The Turkish Government motion allows for an unspecified number of troops to be deployed in Iraq for one year - with the details to be left to Prime Minister Recep Tayyip Erdogan and his ministers.
The issue of sending troops to Iraq is controversial in Turkey and a recent opinion poll indicated that nearly two-thirds of Turks opposed it.
If its troops were to be deployed, Turkey would be the first mainly Muslim nation to send a sizeable force to Iraq.
Bangladesh has vast experience of peacekeeping and uses such missions to promote its image abroad. It is committing troops in Liberia and Ituri, in the Democratic Republic of Congo. Authorities have not yet made a final decision but say a request by the UN for troops is likely to be met with a "positive response".
Pakistan is likely to contribute troops to the multinational force but needs a UN resolution in order to do so. The authorities have not yet made a final decision.
India refused to contribute troops to the US-led coalition force. It has said peacekeepers can only be sent following a stronger UN mandate.
"What Colin Powell has suggested does not constitute a blue-helmet force. We are waiting to see if what is suggested constitutes a specific UN mandate," said an Indian official.
India also wants:
Differentiation between the multinational force and occupying US-led coalition forces
The multinational force to be deployed after a request from the Iraqi people.
Japan's contribution has less to do with politics and more to do with prevailing insecurity in Iraq.
The Japanese parliament approved the deployment of up to 1,000 personnel to help with reconstruction in Iraq, in what would be the largest deployment of Japanese troops overseas since the Second World War. However, their arrival may be postponed, following the recent bombing of the United Nations headquarters in Baghdad.
Thailand, too, may postpone sending troops following the bombing of the UN headquarters in Baghdad.
The official position of Indonesia, which vehemently opposed the US-led invasion of Iraq - is that authorities are waiting for a UN request. Traditionally, Indonesia, the world's most populous Muslim country, contributes troops to UN missions charged with settling specific disputes, rather than enforcing peace.
Mexico - whose membership of the UN Security Council ends this December - is unlikely to contribute troops.