"I am confident we will get one soon," Bush said in a joint news conference with Italian Prime Minister Silvio Berlusconi on Saturday.
Berlusconi said he hoped the UN Security Council would pass a new resolution on Iraq next week.
Bush thanked Berlusconi, one of his closest allies, for his help in drafting the resolution.
"(Berlusconi) fully understands that our troops must be there at the request of a sovereign government," Bush said at the end of a 36-hour visit to Rome, before flying to France for D-Day celebrations.
He did not elaborate further on what he meant by "full sovereignty".
Berlusconi reiterated there was no question of Italy withdrawing its 2700 troops in Iraq.
Thousands of protesters opposed to the US-led occupation of Iraq marched in Rome on Friday.
The possibility of more protests awaited Bush in Paris, where he was to have talks and a working dinner with Chirac, who thwarted his attempt to get a UN Security Council resolution last year authorising war.
Thousands in Italy voiced their
protest against the occupation
Bush's statements came after the Iraqi foreign minister criticised the latest draft UN resolution on Iraq for failing to address the relationship between the new interim government and the multinational force.
Hushiar Zibari said the interim Iraqi government must have some authority over the multinational force in Iraq and that the views of the new US-appointed government should be taken into consideration when major military offensives are undertaken in the country.
On Friday, the United States and Britain revised their UN Security Council resolution on transferring sovereignty to Iraq, giving the country's new interim government authority to order the US-led multinational force to leave at any time.
Zibari also said it was "necessary to spell out what full sovereignty means for the Iraqis".
"Which areas will it cover and which areas are problematic? We have to balance the concept of full sovereignty with our need as Iraqis for the continued presence of the multinational force in our country and what kind of working relations we are going to find out to regulate that relation, because we do need these forces to stay here to help us."
The previous draft introduced on Tuesday declared the council's readiness to terminate the force's mandate by January 2006 or at the request of the transitional government formed after elections held by 31 January 2005.
Zibari says a multinational force
is essential to prevent civil war
The revised draft circulated to Security Council members includes what US Secretary of State Colin Powell and British Prime Minister Tony Blair have stated publicly - that American and British troops will leave if asked.
Zibari said the incoming government wanted the multinational force to stay in Iraq to prevent civil war.
"If you are talking about a sovereign government, at the end of the day really you should have a say in the final status of these forces."
He added that he thought it was important "the relation is organised in a way that the new Iraqi interim government can exercise its authority in terms of undertaking major offensive operations that would have serious security and political repercussions on the country as a whole".
Zibari said he did not see the force leaving before power is transferred to the transitional government early next year.