But Norway rejected the appeal on Saturday, indicating its 180 troops would leave after an American-backed interim Iraqi government takes power on 30 June.
Foreign Minister Jan Petersen said: "We must follow our original plan, of a commitment until the summer."
In the face of worsening violence, three countries - Spain, Honduras and the Dominican Republic - have announced they are pulling out their troops, totalling roughly 2000.
And occupation strength could crumble further because several nations have committed to staying only until the US occupiers transfer power to a selected Iraqi government.
In interviews with media from occupation allies on Friday, Secretary of State Colin Powell acknowledged Norway, the Netherlands and El Salvador - who have almost 2000 troops in Iraq - may not be in Iraq after 1 July.
Powell said a new UN resolution the US was drafting may persuade some nations to extend their tours of duty.
"With a new UN resolution it might be possible for Norway to take another look at the contribution they have made to this effort and perhaps make another contribution or extend the stay."
The resolution is in response to governments' requests that the UN role in Iraq and the international community's relationship with the interim government be made clear.
The US claims it is transferring sovereignty to Iraqis on 30 June.
Washington hopes to slow
international retreat from Iraq
But critics of the plan say Iraq will remain under American occupation because US troops will be outside the control of the interim government.
The forces from most occupation supporters are minimal compared with the 135,000 American troops in Iraq, but their symbolism is large.
During an election campaign stop in Florida on Friday, Bush indicated he was not ultimately concerned what other nations did when it comes to occupying Iraq.
"We're working closely with our friends and allies who understand the stakes.
"But let me make this very clear to you: I will never allow leaders of other nations to determine the national security issues of America," he said.
The US invaded Iraq without explicit authority from the UN and over the objections of major allies.
But it has stressed that its initial invasion and the fact the occupation force comprised troops from more than 30 nations showed international support for the war.