NATO sent at least two large bombs into the sprawling office, residential and military complex where Libyan leader Moammar Gaddafi lives in the heart of Tripoli early Monday, badly damaging at least two buildings but apparently causing no significant injuries.

At the same time, troops loyal to Gaddafi continued their heavy bombardment of the besieged city of Misurata from its southern outskirts on Sunday, after the last of those forces were routed from the city itself, residents and rebels said.

The indiscriminate shelling of the strategic port city over the weekend, some of the heaviest since the siege began in late February, killed at least 58 people, rebels said, belying the Libyan government’s claim that its army was standing aside to let local tribes settle the issue of Misurata.

In Washington, three members of the Senate Armed Services Committee called for immediate military aid for the rebels, stepped-up NATO airstrikes and more direct U.S. involvement, with Sen. Lindsey O. Graham (R-S.C.) saying the alliance should go after Gaddafi himself.

NATO almost seemed to be listening, sending at least two guided bombs just after midnight into the Bab al-Aziziyah complex. Part residence for Gaddafi, part government offices and part military base, the complex is also the scene of nightly celebrations by hundreds of civilians offering themselves as human shields to protect Gaddafi against NATO. Officials at the scene said no one had been badly hurt.

Reporters first heard two huge explosions and saw a red flash from the roof of their hotel in Tripoli. Later they were taken to the scene and saw a destroyed building that officials said contained offices and a library used by Gaddafi. Its roof was caved in and debris was spread over a large area. A fire engine trained water on part of the building, while civilian supporters of the regime, let in with the media members, clambered on the rubble and chanted pro-Gaddafi slogans as dust swirled through the air.

An adjacent building, where Gaddafi met a delegation of South African President Jacob Zuma and four other African presidents looking to broker a peace deal earlier this month, was also badly damaged.

Although the attack may not have been an assassination attempt, it was certainly symbolic. NATO has been striking at Gaddafi’s command and control facilities in recent weeks, although there was no obvious military use for the complex of buildings struck by the bombs.

Early on Sunday, Deputy Foreign Minister Khaled Kaim tried to put a positive gloss on the Libyan army’s retreat in Misurata. He said tribal leaders from the area were angry with the rebels because they could not gain access to Misurata’s port. They wanted to negotiate, he said, but if talks failed, tribal leaders were ready to send in 60,000 armed men to storm the city, in what he feared could be “very, very bloody” warfare.

But Libya is not like Afghanistan or even Iraq, and tribal leaders do not command huge militias they can mobilize in the blink of an eye. Gaddafi, experts said, appeared to be using the tribal issue as a smoke screen to mask his failure to retake Misurata. He was also sending a threat, experts said, both to the citizens of Misurata and anyone abroad who might be thinking of sending in ground troops to protect the city, that he still had the ability to sow chaos by deploying thousands of ground troops, perhaps a mixture of lightly armed civilians and regular soldiers who have shed their uniforms.

“It’s an attempt to spin the rebellion as a tribal issue, but it’s probably not going to work, because what we’ve seen is a broad-based rebellion against Gaddafi,” said Shashank Joshi, an associate fellow of Britain’s Royal United Services Institute. “The other aspect is that it’s a threat.”

British Foreign Secretary William Hague told the BBC he doubted Gaddafi’s forces were really going to withdraw. “This may be cover for using more insurgent type warfare without any uniforms and without tanks.”

Graham and Sens. Joseph I. Lieberman (I-Conn.) and John McCain (R-Ariz) said they interpreted the U.N. Security Council resolution — authorizing military action to protect Libyan civilians and imposing a no-fly zone — as allowing attacks on Libya’s top leadership in Tripoli. “I can’t think of anything that would protect the civilian population of Libya more than the removal of Moammar Gaddafi,” Lieberman told CNN’s “State of the Union.”

Worried that the rebels do not have the momentum to reach Tripoli, Graham suggested that NATO and the Obama administration “go to Tripoli, start bombing Gaddafi’s inner circle, their compounds, their military headquarters.”

But experts said it was unrealistic to expect the West to assassinate the Libyan leader.

“The symbolism of an assassination would be terrible for the United States,” said Joshi, especially after President Obama went to such lengths to secure international support and legal cover for action in Libya and avoid a front-seat role.

Fadel reported from Benghazi.