US Secretary of State Colin Powell has said that Washington is seeking ways of encouraging a greater international contribution to help restore order in Iraq.
The burden of security falls on US shoulders at the moment
Mr Powell was speaking after meeting UN Secretary General Kofi Annan to discuss security arrangements in the aftermath of the bomb attack on the UN building in Baghdad on Tuesday.
Mr Powell said he was exploring the possibility of a new Security Council resolution to persuade members states to "do more" in terms of guaranteeing security in Iraq.
But he brushed aside the possibility of the US ceding more authority to the UN, saying it was not an issue he had discussed with Mr Annan.
TROOPS IN IRAQ
US: More than 140,000
UK: About 12,000
Other nations: About 12,000
Iraqi police, border and security guards: 32,000
But so far any discussion at the UN about giving the organisation a greater say in Iraq's political and economic future has faltered in the face of Washington's determination to keep overall military and political control in American hands, says the BBC's Greg Barrow in New York.
France, Germany, India and Pakistan are among nations who are unwilling to contribute troops to an operation being run by the occupying powers - the US and Britain.
Member states may now want to help the UN more in its hour of need but diplomats say they are still unlikely to contribute troops as long as the United States, rather than the United Nations, maintains overall control, our correspondent says.
Both Japan and Thailand are reported to be considering postponing or cancelling the deployment of the troops they had pledged in the wake of the bombing.
The US Defence Secretary Donald Rumsfeld has said Washington has no plans to add to the more than 140,000 troops already in Iraq.
The death toll from Tuesday's truck bomb on the UN's Baghdad headquarters is now at least 23.
The UN special representative for Iraq, Sergio Vieira de Mello, was among the dead.
"We want UN workers and other workers in Iraq to have a safe environment," Mr Powell said.
"It's a challenging environment but we'll work closely with the United Nations to make sure they can perform their work in as safe an environment as possible considering the circumstances," Mr Powell said.
After meeting Mr Powell, Mr Annan addressed UN staff in New York and said the bomb attack on its headquarters in Iraq was the most deliberate and vicious against its 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.
"We intend to have another facility in town hopefully within
three or four days from where we will be operating," UN humanitarian co-ordinator in Iraq
Romero Lopez da Silva said.
The World Bank and the International Monetary Fund - organisations involved in rebuilding Iraq's economy - have ordered their staff out. The European Commission is also recalling some of its staff.
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.
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 costs
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