The Security Council was expected to discuss the draft resolution behind closed doors, a U.S. official said, speaking on condition of anonymity.
The draft resolution was being presented just hours before President Bush is to lay out his vision for the new Iraqi government in a speech.
It came amid more violence in Baghdad, where two Britons were killed in a bombing outside coalition headquarters, and mortar attacks sent ambulances racing in all directions.
In other developments:
The draft U.N. resolution would give the new Iraqi government the right to review the mandate of the multinational force and control over its oil and gas resources and a fund now in the hands of the United States and Britain where oil revenue has been deposited.
Declaring their determination for a new start for Iraq, the United States and Britain state clearly in the resolution that by June 30, their occupation will end and the Coalition Provisional Authority will "cease to exist." It makes no mention, however, of the Iraqi Governing Council.
On Friday, U.S. deputy ambassador James Cunningham said all council members favored giving Iraq full sovereignty — not "limited sovereignty" as one U.S. official had earlier characterized it.
The United States is retaining ultimate control over Iraq's police, security forces and military, raising concerns at the Security Council — particularly from France and Germany — that the new government will not have enough power and that Iraqis will feel the occupation has not truly ended.
Powell has said the U.S.-led coalition force would leave if the interim government asked it to, though he doesn't expect that to happen.
Cunningham said Friday the new resolution will put the presence of the multinational force "under review and that the Iraqis will have a decisive voice." However, he said there would be no time limit.
The new government "should be given the possibility to decide on security issues, without which this would not be a transfer of sovereignty," German Chancellor Gerhard Schroeder said Monday.
Meanwhile, U.N. envoy Lakhdar Brahimi is trying to get broad agreement on the makeup of the interim Iraqi government due to take power on June 30.
Brahimi will likely announce by the end of this week the names of a president and prime minister, as well as two vice presidents and Cabinet ministers, Iraqi Governing Council member Adnan Pachachi told the Kuwait News Agency Monday.
Filling the top two posts will be Brahimi's most challenging task, since Iraq's three main groups — the Shiite majority and the large Sunni Arab and Kurdish communities — each want a representative as either president or prime minister.
The explosion in Baghdad Monday destroyed a civilian car with armor plating near an entrance to the headquarters of the U.S.-led coalition, killing two people and injuring two others, the U.S. military said. The British Foreign Office said the dead were British civilians.
On Saturday, a suicide car bomber killed four people and slightly wounded a deputy interior minister. On May 17, the president of the Iraqi Governing Council, Izzadine Saleem, was killed along with at least six other people near the coalition headquarters.
Elsewhere, clashes between U.S. forces and fighters loyal to rebel cleric Muqtada al-Sadr overnight in the holy city of Najaf left at least one person dead and 20 injured, a hospital official said.
The toll was likely to rise because ambulances had been dispatched to recover more casualties, according to the official, Fadhil Abbas. He also said the hospital was waiting for relatives of four people killed in clashes the previous night to identify the bodies.
There were no reports of U.S. casualties in the fighting in Najaf, south of Baghdad.
In another holy city, Karbala, militia fighters appeared to have abandoned their positions after weeks of combat.
A U.S. Marine was killed and several other troops were injured when a bomb hidden in a parked car exploded as two American convoys passed Sunday near Fallujah, west of Baghdad.
U.S. troops also battled militiamen in a Shiite district of Baghdad on Sunday. Nine U.S. soldiers were wounded around the city, the military said, including four in a mortar attack in the east of the capital.