WASHINGTON — President Obama worked on Tuesday to bridge differences among allies about how to manage the military campaign in Libya, as airstrikes continued to rock Tripoli. Forces loyal to Col. Muammar el-Qaddafi, however, showed no sign of ending their sieges of rebel-held cities.

On a day when two United States airmen bailed out over Libya and were rescued after the crash of their fighter jet, Mr. Obama and the leaders of Britain and France stepped up efforts to work out an accord on who would be in charge of military operations once the initial onslaught on Libya’s air defense systems was complete.

Mr. Obama reiterated that the United States would step back from the leading role within days, but he also said it was confronting the complexities of running the military campaign with a multilateral force cobbled together quickly and without a clear understanding among its members about their roles.

The president expressed confidence that the coalition would resolve disagreements over the role of NATO, which had flared in recent days over France’s insistence that the alliance not play a leading role in the operation. NATO now seems likely to provide “command and control” functions, but with a separate authority running the operation, which includes Arab and other non-NATO countries.