Three days of heavy airstrikes have highlighted the murky nature of U.S. goals in Libya and opened up new rifts among key members of the international coalition involved in the effort.

Gen. Carter Ham, the U.S. commander leading the operation, said his mission, which was focused on protecting civilians from attacks by regime loyalists, was “pretty clear.” But executing that mission on an increasingly chaotic battlefield that includes opposition forces, government troops and civilians has proved to be dauntingly complex for military commanders.

Commanders, Ham said, have found themselves in the position of having to distinguish between attacks by regime forces on innocent civilians, who clearly require protection, and pitched military battles between rebels and forces loyal to Libyan leader Moammar Gaddafi.

Under the U.N. mandate authorizing the mission, international fighter pilots are not permitted to intervene in battles between Libya’s forces and the loosely organized rebels.

Ham, the head of U.S. Africa Command, acknowledged that making distinctions between fighters and civilians from the vantage of a plane streaking across the sky at 15,000 feet presented risks.

“These are situations that brief much better at headquarters than they do in the cockpit of an aircraft,” he said during a briefing for Pentagon reporters.

Coalition aircraft flew about 80 sorties over Libya on Monday, up from 60 sorties one day earlier. About half of those missions were flown by U.S. pilots, a number that should decline in the coming days as more countries join the coalition effort and the no-fly zone expands east toward the Libyan capital, Tripoli.

The confusion over the mission, meanwhile, has spread beyond Libya. On Monday, NATO members bickered over whether what began as a relatively straightforward effort aimed at preventing Gaddafi from launching airstrikes against his people had turned into a more punitive action directed at his military forces, according to a European diplomat.

The disputes appear to have delayed U.S. efforts to turn the command of the operation over to NATO in the next few days. As of Monday evening, it remained unclear when responsibility would shift and who would assume it.

France, which has sought to portray itself as being in the vanguard of the operation, has raised concerns that Arab states will not participate in the operation if it is led by NATO. Turkey, which abstained from voting on the U.N. resolution, has said it sees no role for NATO.

Senior U.S. officials have made clear that Gaddafi needs to vacate his position even as they have said that driving him from power and degrading his military forces were not the international coalition’s goals.

“I think it’s pretty clear to everybody that Libya would be better off without Gaddafi,” Defense Secretary Robert M. Gates told the Russian news agency Interfax on Monday. “But that is a matter for the Libyans themselves to decide. And I think given the opportunity and the absence of repression, they may well do that.”

Privately, U.S. officials said they hoped that the efforts of the allied forces to enforce the no-fly zone and prevent Libyan regime forces from advancing on rebel-controlled cities would hasten Gaddafi’s demise. “I would not dispute the fact that in some of our actions we are helping the rebels’ cause, but that is not the intent,” said a senior military official.

The final U.N. Security Council resolution authorized member states to take “all necessary measures” to protect civilians and “civilian areas.” The United States, France, Britain and others participating in the initial phase of the operation interpreted that wording to authorize an assault on Gaddafi’s air defense systems and aircraft facilities, as well as the government forces massing outside the eastern city of Benghazi.

President Obama has also said that Gaddafi must pull his troops back from the western cities of Ajdabiya, Misurata and Zawiyah.

On Monday, the president sought to clarify U.S. goals amid mounting criticism from across the political spectrum that he has yet to clearly define the U.S. interest, mission and ambition in Libya.

“The core principle that has to be upheld here is that when the entire international community almost unanimously says that there is a potential humanitarian crisis about to take place, that a leader who has lost his legitimacy decides to turn his military on his own people, that we can’t simply stand by with empty words,” Obama told reporters during a trip to Chile. “That we have to take some sort of action.”

In a letter to Senate Majority Leader Harry Reid (D-Nev.) and House Speaker John Boehner (R-Ohio), he also outlined the reasons for the U.S. military involvement in Libya and underscored its limited scope.

A day earlier, Boehner issued a statement saying that the administration had a “responsibility” to better define the mission in Libya.

Appearing with Chilean President Sebastian Pinera on Monday during his visit to Santiago, Obama suggested that the United States and its international partners had “a wide range of tools” beyond military power to help rebels in their efforts to push Gaddafi from power.

Ham, at the briefing, conceded that it was possible that the Libyan leader could remain in control of at least some portions of his country at the end of the current operation.

“I could see accomplishing the military mission, which has been assigned to me, and the current leader would remain the current leader,” he said. “Is that ideal? I don’t think anyone would say that is ideal, but I could envision that as a possible situation.”

Staff writer Scott Wilson contributed to this report.