Anti-aircraft fire erupted in the Libyan capital on Sunday, marking the start of a second night of international strikes as a defiant Moammar Gadhafi vowed a “long war.” The U.S. military said the allied bombardment so far, using a rain of Tomahawk cruise missiles and strikes by long-range bombers, had been successful in diminishing Gadhafi’s air defenses.

Libya’s rebels were jubilant after the first round of strikes before dawn on Sunday, which came as the overwhelming firepower of Gadhafi’s forces had threatened to crush their month-old uprising.

The strikes gave immediate, if temporary, relief to the besieged rebel capital, Benghazi, in eastern Libya, which the day before had been under a heavy attack that killed at least 120 people.

Airstrikes early Sunday, apparently from French aircraft, devastated a Libyan tank force 12 miles (20 kilometers) south of Benghazi. At least seven demolished tanks were still smoldering in a field hours later, five of them with their turrets and treads blown off, alongside two charred armored personnel carriers and around a dozen damaged jeeps and SUVs of the type often used by Gadhafi fighters.

Rebel fighters climbed on the remains on the tanks, shooting assault rifles in the air in celebration. It was not known how many people were killed in the strike — any bodies had been taken away in the morning — but shredded boots and foam mattresses and tomato paste cans strewn around the scene suggested the Gadhafi forces had been camped at the site when they were hit.

“It was a matter of minutes and Gadhafi’s forces would have been in Benghazi,” said Akram Abdul-Wahab, a 20-year-old butcher in the city.

Soon after nightfall Sunday, heavy anti-aircraft fire rattled over Tripoli, with tracer fire arching into the sky, punctuated by the explosion of shells. The fire suggested a second night of strikes had begun, but it was not immediately known what they targeted.

On state TV, the Libyan armed forces repeated its claim that it ordered a cease-fire — though it appeared that its units continued fighting after a similar cease-fire call the night before.

The rebels hope that the allied intervention will turn the tide in Libya’s conflict, breaking sieges by Gadhafi’s forces on several opposition-held cities and eventually leading to the Libyan leader’s ouster after nearly 42 years in power.

But the Western allies have sent mixed signals over their vision for the end game of their intervention in Libya. France has taken the most aggressive tone, with its U.N. ambassador saying the ultimate goal was to get rid of Gadhafi.

But the top U.S. military officer took a more cautious stance, reflecting American worries about getting dragged deeper into the conflict.

Asked on NBC’s “Meet the Press” whether it was possible that the mission’s goals could be achieved while leaving Gadhafi in power, Adm. Mike Mullen said, “That’s certainly potentially one outcome.” Pressed on this point later in an interview on CNN’s “State of the Union,” Mullen was more vague, saying it was too early to speculate. He said the Libyan leader is “going to have to make some choices about his own future” at some point.

Libya said 48 people were killed in the first round of strikes, including many civilians. That brought criticism of the campaign from the head of the Arab League, which last week took the unprecedented step of calling for a no-fly zone. On Sunday, Arab League chief Amr Moussa criticized the allied strikes, saying they went beyond what the Arab body had supported.

“What happened differs from the no-fly zone objectives,” Moussa told reporters in Cairo. “What we want is civilians’ protection not shelling more civilians.”

Nevertheless, France on Sunday said warplanes in the Arab Gulf nation of Qatar would participate in the air campaign, a sign of continued Arab support.

The U.N. resolution authorizing military action in Libya allows “all necessary means” to protect civilians. That goes far beyond a simple no-fly zone, giving the U.S. and Europeans a free hand in the next stages to attack Gadhafi’s ground forces besieging rebel cities or other military targets.

The first night of strikes began with assaults by French warplanes, followed by a barrage of 112 cruise missiles fired by U.S. and British warships and submarines in the Mediterranean targeting radar systems, communications centers and surface-to-air missile sites. A wave of bombings mainly from American aircraft — including B-2 stealth bombers and F-15 and F-16 fighter-bombers — then targeted Libyan ground forces and air defenses, the U.S. military said. One senior military official said the early judgment was that the attacks had been highly successful, while not fully eliminating the threat posed by Libyan air defenses. The official spoke on condition of anonymity to discuss intelligence data.

The strikes early Sunday hit one of Libya’s main air bases, on Tripoli’s outskirts, the opposition said. Also hit, it said, was an air force complex outside Misrata, the last rebel-held city in western Libya — which has been under siege the past week by Gadhafi forces. Those forces have been bombarding the city from the complex, which houses an air base and a military academy.

Despite the strikes, Gadhafi forces resumed bombarding Misrata after daylight on Sunday, said Switzerland-based Libyan activist Fathi al-Warfali.

“Misrata is the only city in western Libya not under Gadhafi’s control; he is trying hard to change its position,” said al-Warfali, who told The Associated Press he was in touch with residents in the city.

Gadhafi vowed to fight on. In a phone call to Libyan state television Sunday, he said he would not let up on Benghazi and said the government had opened up weapons depots to all Libyans, who were now armed with “automatic weapons, mortars and bombs.” State television said Gadhafi’s supporters were converging on airports as human shields.

“We promise you a long war,” he said.

He called the international assault “simply a colonial crusader aggression that may ignite another large-scale crusader war.”

Throughout the day Sunday, Libyan TV showed a stream of what it said were popular demonstrations in support of Gadhafi in Tripoli and other towns and cities. It showed cars with horns blaring, women ullulating, young men waving green flags and holding up pictures of the Libyan leader. Women and children chanted, “God, Muammar and Libya, that’s it!”

“Our blood is green, not red,” one unidentified woman told the broadcaster, referring to the signature color of Gadhafi’s regime. “He is our father, we will be with him to the last drop of blood. Our blood is green with our love for him.”

In Benghazi, the rebel capital and first city to fall to the uprising that began Feb. 15, people said the strikes happened just in time. Libyan government tanks and troops on Saturday had reached the edges of the city in eastern Libya in fierce fighting that killed more than 120 people according to Gibreil Hewadi, a member of the rebel health committee in Benghazi. He said the dead included rebel fighters and civilians, among them women and children.

Sunday, the city was quiet. As part of the international assault, French warplanes hit targets in the Benghazi area.

Mohammed Faraj, 44, a former military man who joined the rebels, held a grenade in each hand as he manned a checkpoint on the outskirts of the city.

“Me and all of Benghazi, we will die before Gadhafi sets foot here again,” Faraj told The Associated Press. “Our spirits are very high.”

Asked on ABC’s “This Week” if the allied effort aimed to get rid of Gadhafi, France’s ambassador to the United Nations, Gerard Araud, said “We want the Libyan people to be able to express their will, I’ve said … and we consider that it means that Gadhafi has to go.”

Still, the top U.S. military officer said the goals of the international campaign are “limited” and won’t necessarily lead to the ousting of Gadhafi.

Asked on NBC’s “Meet the Press” whether it was possible that the mission’s goals could be achieved while leaving Gadhafi in power, Adm. Mike Mullen said, “That’s certainly potentially one outcome.” Pressed on this point later in an interview on CNN’s “State of the Union,” Mullen was more vague, saying it was too early to speculate. He said the Libyan leader is “going to have to make some choices about his own future” at some point.