The Libyan government has accused Nato of trying to assassinate Muammar Gaddafi after two air strikes in three days hit sites in or near the compound where he is believed to direct military strategy.

At least two large missiles or bombs struck a multistorey office building in Bab al-Azizia, the sprawling complex in the centre of Tripoli, shortly after midnight yesterday. The Libyan government claimed three people were killed in the attack, although some officials there shortly after the strike said there had been no injuries.

"We regard it as an attempt to assassinate the leader and unifying figure of this country," government spokesman Moussa Ibrahim said, standing before the skeleton of the bombed building. "It was not a civilised act. This is an act of terrorism, an act worthy of mafia gangs, not governments."

The targeted building housed document archives and a library regularly used by Gaddafi, according to officials. Its roof caved under the impact of the strike; the ground over a wide area was covered in shattered masonry, broken glass and metal, and pools of water that had formed between piles of rubble. Three hours after the blast, thick dust was still in the air when foreign journalists were taken to the site.

Figures close to the regime believe that Nato is targeting Gaddafi and his inner circle in violation of the UN security council resolution authorising military intervention to protect civilians. The Libyan leader has rarely been seen in public since the crisis began around 10 weeks ago.

Ibrahim refused to comment on Gaddafi's whereabouts, other than to say he was "in a safe place", working from Tripoli and leading the battle for peace and democracy in Libya. The leader was in good health and high spirits, he added.

Hours before the strikes, US senator Lindsey Graham called for Nato to "cut the head of the snake off". Gaddafi "needs to wake up every day wondering 'will this be my last?'" the Republican member of the armed services committee told CNN.

The strike came as Liam Fox, the defence secretary, heads to the US for talks on the military campaign with his counterpart Robert Gates. The discussions are expected to focus on the best way of stepping up Nato attacks on Gaddafi's forces, after the US decided to bring its Predator drones into operation.

Nato headquarters in Brussels confirmed the attack on the Gaddafi compound, describing the buildings as a legitimate target under the terms of the UN mandate empowering it to hit regime facilities that threaten the safety of Libyan civilians.

"We can confirm that the alliance carried out a precision air strike in central Tripoli," said Nato. The target was "a communications headquarters used to co-ordinate attacks against the civilian population … We have no evidence of any civilian casualties."

The official said the attack was part of a strategy of varying the targets selected for striking in Libya as part of the campaign to "degrade the regime forces".

Italy, which has been playing a reduced role in operations, decided on Monday that its air force will be allowed to bomb selected military targets in Libya. A statement from Silvio Berlusconi's office said he had informed Barack Obama in a telephone conversation of the decision and that he would call other European leaders to tell them personally as well.

Saif al-Islam Gaddafi, the Libyan leader's son, said the air strikes on Gaddafi's seat of power would make Libya stronger. "It's impossible that it will make us afraid or give up or raise the white flag," the Jana state news agency quoted him as saying. "In history, no country has achieved victory with spies and traitors and collaborators … Nato, you are the losers."

At Gaddafi's compound, supporters who gather nightly to act as human shields against the air strikes climbed on the shattered building shortly after the blasts, as chunks of masonry fell. They waved loyalist green flags and chanted pro-Gaddafi and anti-Nato slogans.

The foreign media was refused free access to the site, where shelves of files could be seen hanging in the carcass of the building. "Any government has secret archives and documents. We are still looking after our documents," said Ibrahim.

Another building, a ceremonial reception area where Gaddafi hosted a delegation from the African Union two weeks ago, including South African president Jacob Zuma, was damaged. Journalists were barred from inspecting a third damaged building.

A compound housing Libyan state television was hit in a separate strike near Tripoli's old city, according to an official. Broadcasts went off air temporarily as a result, he said.

The strike on Bab al-Azizia is the second time Nato has struck inside the compound since its military campaign started. A missile hit a command-and-control building in the early days of the strikes, causing extensive damage.

In the early hours of Saturday, two missiles hit a site a few hundred metres from the compound. Nato appeared to have targeted an underground bunker, which was visible from the craters caused by the missiles.

The strike on Gaddafi's compound followed two days of heavy assault on the besieged city of Misrata by government forces. Despite the Libyan government's claims that troops had pulled back from the city, forces on the ground stepped up shelling and rocket fire after gains made on the ground by rebels. Two schools are reported to have been destroyed by shelling.

"Now Gaddafi's troops are on the outskirts of Misrata, using rocket launchers," a resident named Abdel Salam told the Associated Press.