A senior US military official told CBS News that the military action in Libya is truly an international operation, of which NATO will only play a part.
"We're still in the process of sorting through the exact structure," the official said.
One of the biggest questions is who will lead the ongoing effort, as President Barack Obama and other administration officials have insisted that the US plans to step into the background as swiftly as possible. British Prime Minister David Cameron's office said that he and Mr. Obama agreed that NATO should play a key role in commanding the military campaign in Libya. France's Nicolas Sarkozy has been a little more moderate, only agreeing that NATO will have a role.
Recently, Turkey, a NATO member, finally came around to agreeing with France that NATO should be involved militarily after initially blocking attempts to formally do so. Turkey's prime minister had repeated Arab world concerns recently that outside military involvement could turn into a grab for resources if and when Muammar Qaddafi is deposed.
That objection seems to have passed, however, as Qatar has recently sent airplanes to involve themselves in the currently semi-disorganized coalition effort in Libya. A senior US military official told CBS News that he believes more Arab states will be joining the effort shortly.
In the meantime, France has proposed the creation of a committee to run the operation. French Foreign Minister Alain Juppe said Tuesday that the new body would bring together foreign ministers of participating states - such as Britain, France and the U.S. - as well as the Arab League. It is expected to meet in coming days, either in Brussels, London or Paris, he added.
Any committee's job will be to bring order to a mission which some observers see as a chaotic effort by member nations with differing objectives - they are in agreement on getting rid of Qaddafi, who has ruled Libya for 42 years, but disagree on whether that should be a goal of military action.
Shashank Joshia, an analyst with London-based Royal United Services Institute, says the situation is further confused because the U.S. wants to take a back seat for the first time in years.
Still, as member nations strove to find a common military aim Tuesday, NATO did agree on one action - to have its warships begin enforcing the U.N. arms embargo. A flotilla consisting of frigates, minesweepers and other ships already in the Mediterranean has been given the mission.
But two diplomats, who asked not to be named because they were not authorized to speak to the media, said agreement had not yet been reached on whether the alliance should take over enforcement of the no-fly zone, which the U.N. Security Council also approved last week in an effort to prevent government jets from bombing civilians.
NATO, with its vast staffing and experience in coordinating multinational operations, could fill the leading role, most observers agree, but France and Turkey, both of whom are members, are opposed to NATO taking over. And it would need the approval of all the alliance's 28 members to take such action.
Turkey has blocked the approval, seeking to narrow the mission and ensure that no foreign occupation of Libya would result. And France has said NATO's reputation in the Muslim world is tainted by its military effort in Afghanistan.
In addition, France has historically been uncomfortable with NATO, and only rejoined the alliance's military wing two years ago, after having sat on the sidelines for the previous 42 years.
Nevertheless, Juppe, the French foreign minister said that through the new steering committee the coalition would avail itself of the military alliance's planning and intervention capabilities.
"For us, the intervention is firstly an operation wanted by the United Nations... It is run by a coalition of member-states, all of whom are not members of the North Atlantic Treaty Organization," Juppe said.
"This is, therefore, not a NATO operation, even if it must be able to rely on military planning and intervention capacities of the Alliance."
Juppe said that French President Nicolas Sarkozy had proposed the creation of the new body and Britain had agreed to it.
Paris and London pressed early on for a no-fly zone to protect Libyan civilians from attacks by forces loyal to Moammar Gadhafi. France also took a lead role on Saturday, when it hosted a summit of nations participating in the coalition - just before the first bombing runs over the North African country by French fighter jets.