Libyan government spokesman Ibrahim Musa said the strike had targeted an "administrative building"
Allied forces carrying out air strikes in Libya say Colonel Muammar Gaddafi himself is not a target, despite an overnight attack against his compound.
The chief of UK armed forces said attacks on Libya's leader were "not allowed" under a UN resolution calling for the protection of Libyan civilians.
And a French spokesman said that even if the Libyan leader's exact location was known, he would not be fired on.
Col Gaddafi has been fighting a rebellion that broke out last month.Tripoli complex hit
On Sunday UK Defence Secretary Liam Fox said targeting Col Gaddafi could "potentially be a possibility".
But on Monday Britain's Chief of Defence Staff, Sir David Richards, said he was "absolutely not" a target. "It's not allowed under the UN resolution," he added.
At the scene
Two allied raids on Tripoli provoked heavy barrages of anti-aircraft fire aimed at missiles and aircraft that we in the city could neither see nor hear.
The city echoed with gunfire and the sky lit up with the red glow of tracer rounds. Several loud explosions rocked the city, including one at Col Gaddafi's own residential compound.
The compound had filled up with enthusiastic supporters of Col Gaddafi only the previous day - civilians who said they were ready to die with him if necessary.
It is not known whether any of them were still in the compound when the missiles struck. Some journalists were taken to the site during the night.
A Libyan government spokesman said it was proof the allies were targeting non-military locations. The removal of Col Gaddafi is not a stated aim of the UN Security Council resolution. But this strike is a reminder that he is not safe from the allied air strikes.
The document, approved by the Security Council last week, authorises "all necessary measures" to protect civilians from pro-Gaddafi forces - including a no-fly zone.
A French defence ministry spokesman, Laurent Tesseire, also said the aim of the strikes was solely to protect civilians and Col Gaddafi himself was not a target.
Asked by French radio whether the Libyan leader would be fired on if his exact whereabouts was known, he said: "The answer to that is no."
The comments came after a second night of US-led action in Libya. Ten to 12 missiles were fired, a spokesman for the US Africa Command said.
In Tripoli, Col Gaddafi's sprawling Bab al-Aziziya complex was hit. Western journalists taken to the compound were shown a ruined building.
An official from one of the coalition countries, who asked not to be named, told journalists the strike had destroyed Col Gaddafi's "command and control capability".
Between 70 and 80 coalition sorties were flown on Monday.
Although the coalition has said that ground forces moving on rebel positions are open to attack, the head of the US Africa Command, Gen Carter F Ham, said on Monday that there had been no direct co-ordination with anti-Gaddafi rebels.
He also said the no-fly zone over Libya would soon expand to cover a 1,000-km area.
The action against Col Gaddafi began on Saturday with French air strikes in the east. A barrage of cruise missiles, launched from US and British surface ships and submarines followed.'Misinterpreted'
In Moscow, Russian Prime Minister Vladimir Putin condemned the UN resolution as "flawed".
"It allows everything," he said on Monday. "It resembles medieval calls for crusades." Russia abstained during the Security Council vote on the resolution last week.
The BBC's Steve Rosenberg in Moscow says Mr Putin's strong criticism may be designed to distance himself from President Dmitry Medvedev's foreign policy decisions and boost his own domestic popularity by talking tough.
Mr Medvedev said Mr Putin's use of the word "crusade" was unacceptable.
Arab League Secretary General Amr Moussa, who had previously appeared to criticise the coalition air strikes, said on Monday his comments had been "misinterpreted" and that the league was "committed to UN Security Council Resolution 1973".
Diplomats say a UN Security Council meeting will be held behind closed doors on Monday to discuss the Libyan situation.
Envoys from Nato met in Brussels on Monday to try to sort out any differences of strategy, amid concerns from Turkey in particular about military involvement.
But French Foreign Minister Alain Juppe said Nato would be ready to support the coalition within "a few days".
Renewed fighting was reported in Misrata, 200km (130 miles) east of Tripoli, on Monday.
The city has been under siege by government troops and rebel spokesmen said pro-Gaddafi forces were using "overwhelming firepower" and had bombarded the city for a fourth day.
One told the BBC that Col Gaddafi "only controls the main street that leads all the way out of Misrata. He is controlling that street from end to end and he's preserving his supply line".
Separate rebel spokesmen said there had been between nine and 11 deaths at the hands of pro-Gaddafi forces but the reports cannot be independently confirmed.
There were reports that pro-Gaddafi forces were bringing civilians to Misrata from outlying areas to deter further allied strikes.
Col Gaddafi has ruled Libya for more than 40 years. An uprising against him began after the long-time leaders of neighbouring Tunisia and Egypt were toppled.
Are you in Libya? What do you think about the air strikes? Send us your experiences and comments.
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