Cunningham told the UN Security Council there will clearly be a need for international forces beyond next month.
"Coordination and consultative arrangements will be established between the [multinational force] and the sovereign interim government of Iraq. The fight against terror and for Iraq's security and stability will be a shared fight," Cunningham said.
U.S. officials have stressed the need for unified command under U.S. leadership. But Russia, France, and other Security Council members say Iraqi officials must have control over their own forces.
A council resolution in the coming weeks is expected to clarify the military arrangements.
Cunningham also told the council that many Iraqis have expressed a desire to have limits on the authority of the interim government, leaving major decisions to an elected Iraqi government. He said it is up to Iraqis to decide on those limits of power, as part of their consultations with UN envoy Lakhdar Brahimi.
Cunningham appealed for an expansion of the international security force to support the return of more UN personnel to Iraq.
He said U.S. officials are working to establish a unit within the multinational force under unified command to provide security for UN personnel and facilities in Iraq.
"The ability of the United Nations to continue its vital role in assisting Iraqis to prepare for elections depends on its security. We urge the international community to participate in this important task," Cunningham said.
Few states have so far committed to such a force. Pakistan, the current president of the Security Council, has been asked by Washington to contribute but is awaiting the outcome of the upcoming council resolution.
Pakistan's UN ambassador, Munir Akram, told reporters today the key aspect is the support of Iraqis for such a force.
"We would need to see how the transition is made, how acceptable that is to the Iraqi people before we can make a decision on that. Obviously, we would not go into a situation if it is not acceptable to the Iraqi people," Akram said.
The UN election team in Iraq is currently selecting Iraqis to serve on an independent election commission.
The posts include seven commissioners and a chief electoral officer. UN officials say they have received the names of nearly 1,900 candidates from the country's 18 governorates.
UN experts will choose a list of finalists and Coalition Provisional Authority head L. Paul Bremer will make the final selections by the end of this month. The commission is to guide the country toward elections early next year.
A separate UN mission led by Brahimi is seeking to shape consensus among Iraqis for the interim government to assume power on 30 June. Leading members of that government are also to be chosen by month's end by UN and CPA officials.
Britain's UN ambassador Emyr Jones Parry urged the Security Council to unite behind a resolution endorsing the new Iraqi administration.
"That resolution should clearly mark the move to a sovereign interim Iraqi government and it should also mark our whole-hearted support for that government and for continued Iraqi progress towards democratic elections," Jones Parry said.
Earlier today, Iraqi Foreign Minister Hoshyar al-Zebari underlined the need for coalition troops to maintain security in Iraq. But he also stressed the importance of a genuine transfer of sovereignty on 30 June 30.