Having largely succeeded in stopping a rout of Libya’s rebels, the inchoate coalition attacking Col. Muammar el-Qaddafi’s forces remains divided over the ultimate goal — and exit strategy — of what officials acknowledged Thursday would be a military campaign that could last for weeks.
The United States has all but called for Colonel Qaddafi's overthrow from within — with American commanders on Thursday openly calling on the Libyan military to stop following orders — even as administration officials insist that is not the explicit objective of the bombing, and that their immediate goal is more narrowly defined.
France has gone further, recognizing the Libyan rebels as the country's legitimate representatives, but other allies, even those opposed to Colonel Qaddafi's erratic and authoritarian rule, have balked. That has complicated the planning and execution of the military campaign and left its objective ill defined for now.
Only on Thursday, the sixth day of air and missile strikes, did the allies reach an agreement to give command of the "no-fly" operation to NATO after days of public quarreling that exposed the divisions among the alliance's members.
"From the start, President Obama has stated that the role of the U.S. military would be limited in time and scope," Secretary of State Hillary Rodham Clinton said Thursday evening in announcing the plan.
But even that agreement — brokered by Mrs. Clinton and the foreign ministers of Britain, France and Turkey — frayed almost immediately over how far the military campaign should go in trying to erode the remaining pillars of Colonel Qaddafi's power by striking his forces on the ground and those devoted to protecting him. It was salvaged, one diplomat said, only by papering over the differences concerning the crucial question of who actually controls military strikes on Libya's ground forces.
"There were differences in the scope of what NATO would do and what would remain with the national militaries," a senior administration official said, expressing hope that the agreement on NATO command would be a step toward resolving them.
The questions swirling around the operation's command mirrored the larger strategic divisions over how exactly the coalition will bring it to an end — or even what the end might look like, and whether it might even conceivably include a Libya with Colonel Qaddafi remaining in some capacity. While few countries have openly sided with the Libyan leader, officials said on Thursday that most of the allies expected that the use of military force would lead to talks between the government and the rebels.
"I don't think anyone is ruling out some kind of negotiated settlement," the official said. Colonel Qaddafi has responded defiantly, making the likelihood of his negotiated departure seem exceedingly remote.
The allied bombardment remains in its early stages. It has already badly eroded Libya's combat power — with scores of missile and airstrikes against Libya's air defenses and armored columns — but not yet drastically reversed the military equation on the ground.
Mr. Obama, having returned from his trip to Latin America on Wednesday, met privately at the White House with his senior national security officials, but he made no public statements, even as reservations percolated in Congress and elsewhere about the conflict and its end game.
Asked about concerns raised the day before in a letter by the House speaker, John A. Boehner, Mr. Obama's spokesman, Jay Carney, said, "I think the president's been very clear, and he has been asked and answered this question numerous times."
In fact, Mr. Obama has not made clear what will happen if the international coalition succeeds in establishing control of the skies over Libya, but Colonel Qaddafi's loyalists and rebels continue to attack and counterattack each other in a bloody, protracted stalemate.
"We should never begin an operation without knowing how we stand down," said Joseph W. Ralston, a retired general who served as NATO commander and vice chairman of the Joint Chiefs of Staff. "We did a no-fly zone over Iraq for 12 years and it did nothing to get rid of Saddam. So why do we think it will get rid of Qaddafi?"
In Paris, the French foreign minister, Alain Juppé, expressed confidence in the success of the operation so far, even as he urged patience. "The destruction of Qaddafi's military capacity is a matter of days or weeks, certainly not months," he told reporters, adding: "You can't achieve our objective in just five days."
But any exit strategy will depend on the climate on the ground, and whether rebel forces can be effective in defending themselves without international support. So far, the rebels in the east have failed to punch through the line of Qaddafi forces at the strategic city of Ajdabiya, even with foreign forces battering Libya's air and ground forces. In one potentially significant shift in momentum, the rebels were negotiating the surrender or withdrawal of one unit of Qaddafi troops in Ajdabiya. "We are trying to lead them to peace," said a rebel spokesman, Col. Ahmed Omar Bani.
In the western commercial center of Misrata, though, rebels say that airstrikes from international forces will enable them to fight off the Qaddafi siege but not to march to Tripoli, which remains a Qaddafi stronghold. Still, a rebel spokesman who has identified himself by only his first name, Mohammed, predicted that residents of Tripoli would rise up soon. "I know the situation there is really simmering," he said by telephone. "They have seen the dictator's murderous ways, and they feel his days are numbered."
In Tripoli, a few residents critical of the Qaddafi government — all speaking covertly, for fear of reprisals — said that coalition attacks had emboldened people there, who plan new protests after midday prayers on Friday.
But others said the intervention might have arrived too late to set off a popular uprising. "I do not think Tripolitanians will rise," one Libyan opposition figure with ties around Tripoli said, also speaking on condition of anonymity out of fear, citing the reprisals that the city's neighborhoods had already endured.
From the start, the administration insisted that it was acting to avert the imminent slaughter of civilians in Benghazi and other rebel-held cities, and that the goal of the military operations was clearly spelled out in the United Nations Security Council resolution.
Mr. Obama's administration, however, has clearly tried to avoid the debate over a strategy beyond that by shifting the burden of enforcing the United Nations Security Council resolution authorizing force on to France, Britain and other allies, including Arab nations like Qatar and the United Arab Emirates, which on Thursday said that it would contribute warplanes to the effort. In other words, the American exit strategy is not necessarily the coalition's exit strategy.
"We didn't want to get sucked into an operation with uncertainty at the end," the senior administration official said. "In some ways, how it turns out is not on our shoulders."
Even so, no matter who is in charge American aircraft and warships will continue to support the campaigns for weeks or months, conducting surveillance, refueling and search and rescue operations that the United States is better able to do. And in the event that the allied mission goes badly awry, there would be little doubt that the American forces would return to the fight.
Steven Lee Myers reported from Washington, and David D. Kirkpatrick from Tripoli, Libya. Eric Schmitt and Mark Landler contributed reporting from Washington.
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