France says that if the United States wants other countries to send troops to Iraq, it needs to share sensitive information and the military command.
France points the finger at the US for Iraq's lawlessness
"Sharing the burden and the responsibilities in a world of equal and sovereign nations means also sharing information and authority," France's deputy ambassador to the United Nations, Michel Duclos, said.
The Americans are working on a new UN resolution which would authorise an expanded international force to provide security in Iraq.
Several countries - reported to include Germany and Russia - say they want to help, but not if their troops have to serve under the US military.
The US Secretary of State Colin Powell has said there are no plans to cede authority to the UN.
Meanwhile, the UN's own security co-ordinator, Tun Myat, is being sent to Baghdad to assess whether it is safe for UN staff to stay in the city in the wake of Tuesday's bomb attack at the UN headquarters.
Chain of command
The truck bombing is thought to have shaken up efforts to establish a clear line for the organisation in the country whilst debate increases over control of the country, correspondents say.
UK Foreign Secretary Jack Straw has said the United States must keep command of the joint military force in Iraq despite the calls for a larger role for the UN.
Speaking at UN headquarters in New York on Thursday, Mr Straw said the Americans had more troops in Iraq than any other country and "if you want there to be an effective military operation... the command has to be through the United States".
France, Russia, China and Germany are pressing for an expanding of the UN mandate in Iraq beyond humanitarian aid and reconstruction.
Mr Duclos questioned whether "we would be in this state" had coalition forces waited to establish an international partnership under UN guidance before launching its attack on Iraq in March.
India and Pakistan are also among nations who are unwilling to contribute troops to an operation being run by the US and Britain.
Both Japan and Thailand are also reported to be considering postponing or cancelling the deployment of the troops they had pledged in the wake of Tuesday's attack.
Mr Powell met UN Secretary General Kofi Annan on Thursday to discuss security arrangements in the wake of the bomb attack.
Meanwhile, a senior US official in Baghdad told The New York Times that investigators were examining the possibility that Iraqi security guards employed by the UN might have helped the bombers.
"We believe the UN's security was seriously compromised," the official was quoted as saying. "We have serious concerns about the placement of the vehicle [which carried the bomb]", he added.
US investigators at the scene of the blast said they had found human remains inside the truck used in the blast, heightening speculation it was a suicide bombing.
On Thursday, the Dubai-based al-Arabiya television station said it had received a statement from a previously unknown group, the Armed Vanguards of the Second Muhammad Army, claming responsibility for the attack.
After meeting Mr Powell, Mr Annan told UN staff in New York that the bomb attack in Iraq was the most deliberate and vicious against UN workers in the organisation's history.
UN staff are to resume normal operations in Iraq from Saturday.
The number of UN staff is being reduced in Iraq by about 100 and some administrative staff will be moving to bases in Jordan and Cyprus, a UN official said.
PLANNED MULTI-NATIONAL FORCE FOR IRAQ
Multi-national force: This will be the largest mission of its kind to take place without UN co-ordination or
central Nato command
Cost: US reportedly expected to pay partner nations a total of more than $200m in airlift and support
Twenty-seven nations have sent troops:
Albania, Azerbaijan, Bulgaria, the Czech Republic, Denmark, the
Dominican Republic, El Salvador, Estonia, Georgia, Honduras,
Hungary, Italy, Kazakhstan, Latvia, Lithuania, Macedonia, Mongolia,
the Netherlands, Nicaragua, Norway, Poland, Romania, Slovakia, South
Korea, Spain, UK, Ukraine
Five nations' troops are expected:
Japan, Moldova, Philippines, Portugal and Thailand