THE MUDDLE of U.S. policy in Libya was inadvertently encapsulated by Gen. Carter Ham, the commander of the operation, in a news briefing Monday. Gen. Ham said that if a Libyan opposition supporter carrying an AK-47 defended his home against the forces of Moammar Gaddafi, U.S. and allied pilots would protect him. But if he were operating a military vehicle or heavy weapons, he would get no support, because “we do not provide close air support for the opposition forces.”

Does that sound clear? Gen. Ham doesn’t seem to think so. “It’s a very problematic situation,” he said. “Sometimes these are situations that brief better at the headquarters than in the cockpit of an aircraft.”

Or at the presidential podium. “I think it’s very easy to square our military actions and our stated policies,” President Obama insisted during a stop in his tour of Latin America. “U.S. policy,” he reiterated, is “that Gaddafi needs to go.” But the military intervention in Libya — which has included a strike on the dictator’s personal compound in Tripoli — is not aimed at that goal, the president maintained. Instead, in keeping with its U.N. mandate, it has been limited to protecting Libya’s civilian population.

As a practical matter, the attempt to draw that distinction for pilots operating at 30,000 feet has rendered the military intervention less effective than it might be. U.S., French and British airstrikes did succeed in driving Gaddafi forces away from the rebel-held city of Benghazi, and thus prevented the threatened bloodbath that finally convinced Mr. Obama that military action was necessary. But opposition supporters in the city of Misurata, many of them civilians, said Tuesday they had gotten no help even though they were under attack from the regime’s tanks and artillery. Meanwhile, the strikes that did take place prompted objections from Russia, China and the Arab League.

The administration’s principal response to this mess has been to try turning over the mission to its allies as quickly as possible — an effort that triggered a multinational quarrel over who would take over command from Gen. Ham. But another abdication of leadership won’t free Mr. Obama from Libya for long. Because of its limits, the military intervention threatens to perpetuate a stalemate that leaves Mr. Gaddafi in power, and that over time would create both a greater humanitarian crisis and more serious threats to U.S. and European interests. It was Secretary of State Hillary Rodham Clinton who this month warned that Libya could become “a giant Somalia,” riven by tribal warfare and anarchy that allows al-Qaeda to create a stronghold.

The only solution to Libya’s crisis, as Mr. Obama first recognized several weeks ago, is the removal of Mr. Gaddafi from power. But the administration still seems to lack a coherent strategy for accomplishing that aim. Mr. Obama spoke vaguely on Monday about “a wide range of tools” and “a powerful international consensus around the isolation of Mr. Gaddafi.” But financial sanctions and an arms embargo are not likely to force him out. Appeals to the dictator’s collaborators to turn against him have been undermined by public predictions by senior U.S. officials, most recently Gen. Ham, that he might remain in office.

Were it determined to accomplish its stated aim, there is much more the administration could do. It could provide arms to the rebels and also follow France’s lead in recognizing the Benghazi-based government. It could take advantage of the broad language in the U.N. resolution to take more aggressive action against the regime’s military assets, striking armor, artillery and aircraft wherever they could be found. Currently, according to Gen. Ham, Gaddafi tanks are to be attacked only when they are advancing against civilians. Rebel forces appeared close to victory several weeks ago; if the regime’s heavy weapons were systematically targeted, the rebels could surge forward again.

All this would require Mr. Obama to do something he has avoided from the beginning in Libya: Exercise U.S. leadership. The president’s defenders say he has refused to embrace that role because he wants any intervention to enjoy broad support, and because he seeks to change the U.S. image in the Middle East. But as initial operations in Libya have demonstrated, effective multilateral action, especially involving the military, depends on strong American participation.

Far from rejecting that role, many Arabs have been puzzled and even outraged by Mr. Obama’s manifest reluctance to support a revolution aimed at overthrowing one of the region’s most vile dictatorships. Ultimately Mr. Obama’s passivity is self-defeating. The sooner he recognizes this, the better the chance of salvaging a decent outcome in Libya.