U.S. and allied warplanes continued pounding Libya’s air defenses Sunday and launched deadly strikes against ground forces as Libyan leader Moammar Gadhafi offered no serious military challenge to the establishment of a no-fly zone over his country.

“We judge these strikes to have been very effective in significantly degrading the regime’s air defense capability,” Vice Adm. Bill Gortney, director of the Pentagon’s Joint Chiefs of Staff, said Sunday.

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Libyans celebrate atop a tank belonging to the forces of Moammar Gadhafi on the outskirts of Benghazi in eastern Libya on Sunday after the tanks were destroyed by U.S. and allied planes. The Associated Press

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• Now the question becomes: How will Libyan campaign end?

If the military gains were clear, the international and domestic political support for the U.N.-authorized campaign seemed to weaken. The Arab League voiced concern about civilian deaths, and leading Republicans demanded clarity on the ultimate goals.

President Obama has declared that Gadhafi “must leave,” but Joint Chiefs of Staff Chairman Mike Mullen, the administration’s most visible spokesman Sunday, acknowledged that the outcome of the conflict remains uncertain.

A missile struck a building on Sunday night in the compound where Gadhafi lives, fueling the rage that has erupted among his supporters since U.N.-mandated airstrikes began on Saturday.

A plume of smoke was seen rising from the Bab al-Aziziya compound, a walled, fortified enclave on the southwestern edge of the city where the Libyan leader lives.

The building was an administrative one located near the tent where Gadhafi receives visitors, and at the time a couple of hundred of his supporters were in the compound nearby, acting as human shields.

The attack took place as Mullen told reporters in Washington that “we’re not targeting (Gadhafi’s) residence.”

But the compound may have been struck by missiles fired by British or French forces, which have taken the lead in pursuing the effort to halt attacks by Libyan forces against rebels seeking to topple Gadhafi. CNN quoted “coalition sources” in Washington as saying that the building was hit because it contained “command and control” capabilities.

Air Force B-2 stealth bombers as well as Marine Harrier jets flying from a ship in the Mediterranean followed up on the dozens of Tomahawk cruise-missile strikes that opened the assault on Libya, called Operation Odyssey Dawn.

U.S. fighter jets mounted attacks on Libyan soldiers advancing on the rebel-held city of Benghazi as part of a broader mission to protect the opposition forces from being overrun, said a senior U.S. military official.

The strikes, which were carried out by 15 U.S. fighter jets as well as French and British planes, left a smoking graveyard of military vehicles outside Benghazi.

“We thank the international community for their serious steps to kill this murderer,” said Adam al-Libi, an opposition fighter in the rebel capital. “If God is willing, we will win.”

The United States also mounted strikes with satellite-guided bombs on an airfield outside the coastal city of Misurata, where the Libyan air force maintained fighter jets in hardened shelters. Gadhafi continued to keep the Soviet-era fighters on the ground and the United States detected no radar emissions from any of the air defense sites that it had targeted, military officials said.

The attacks’ intensity startled the 22-member Arab League, which had backed the creation of a no-fly zone. Secretary General Amr Moussa called an emergency meeting of the organization after a bombardment that he said “led to the deaths and injuries of many Libyan civilians.”

“What is happening in Libya differs from the aim of imposing a no-fly zone, and what we want is the protection of civilians and not the bombardment of more civilians,” said Moussa, according to Egypt’s state news agency.

Mullen said he had seen no evidence that the attacks had caused civilian casualties but charged that Gadhafi had created human shields around radar and missile sites.

The Libyan leader continued voicing defiance and vowed to conduct a “long, drawn-out war.”

“We will not leave our land, and we will liberate it,” he said on state television. “We will remain alive, and you will all die.”

Libya’s armed forces commanded all units to observe an immediate cease-fire, a Libyan army spokesman said. An earlier announcement of a cease-fire proved short-lived.

Republican leaders, who had backed military action and have said they would like to see Gadhafi fall, criticized the administration, saying the bombing campaign has no clearly defined goal.

“Before any further military commitments are made, the administration must do a better job of communicating to the American people and to Congress about our mission in Libya and how it will be achieved,” said House Speaker John Boehner, R-Ohio.

Asked on CBS’ “Face the Nation” whether the campaign could lead to a stalemate, Mullen left open the possibility that Gadhafi could remain in power.

“He’s a thug. He’s a cagey guy. He’s a survivor. We know that,” Mullen said. “So it’s difficult to know exactly how it comes out.”

Democrats said the intervention was designed to be limited and focused on humanitarian objectives.

“The goal of this mission is not to get rid of Gadhafi, and that is not what the U.N. licensed. And I would not call it going to war,” Sen. John Kerry, D-Mass., Senate Foreign Relations Committee chairman, said Sunday on NBC’s “Meet the Press.”

Defense Secretary Robert Gates said the United States expects to turn control of the mission over to a coalition — probably headed either by the French and British or by NATO — “in a matter of days.”

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