"I want to say to the Crusader cowards that I live in a place where I cannot be reached or killed; I live in the hearts of millions," Qaddafi said in the message broadcast on state television.
A series of six loud explosions rocked Tripoli late Friday and early Saturday as jets flew overhead. Smoke could be seen rising from one of the sites in eastern Tripoli, witnesses said.
Air raids have rocked the Libyan capital almost nightly, stepping up the pressure on the Qaddafi regime.
In Washington, the Libyan rebel movement's number two, Mahmud Jibril, was received at the White House by President Barack Obama's national security advisor.
The White House said the rebels' National Transitional Council was a "legitimate and credible" voice of the Libyan people. But it stopped short of offering the full diplomatic recognition that Jibril was seeking.
Questions about Qaddafi's fate arose earlier Friday when Italian Foreign Minister Franco Frattini said Qaddafi was "probably outside of Tripoli and probably also injured."
He said the reports that Qaddafi was on the run were credible because they came from the Roman Catholic bishop of Tripoli. But the bishop, Giovanni Martinelli, later denied having made any such comment to Frattini.
"What the foreign minister said is not right because I never said that the Libyan leader was wounded," Martinelli told Radio France Internationale.
"I only said that he was under psychological shock from the death of his son. I did not say he was wounded or that he left Tripoli."
Libyan government spokesman Mussa Ibrahim told journalists in the capital that Qaddafi "is in very good health, high morale, high spirits," and "he is in Tripoli."
Qaddafi's audio message appeared to have been made sometime after a NATO strike on his Bab al-Aziziya compound early Thursday, because Qaddafi referred to its having "led to the martyrdom of three civilians, journalists."
Frattini said international pressure was causing "the disintegration of the regime from the inside, which is what we wanted."
He added that arms depots had been raided by rebels on the outskirts of Tripoli in the past few hours.
Meanwhile, Ibrahim told the news conference in Tripoli that a NATO air strike had killed 11 imams who had gathered in Brega, putting the number of wounded people at 50, including five in critical condition.
A spokesman in Brussels said the Western military alliance had no information on the veracity of the claim.
At the news conference, an imam identified as Nureddin al-Mijrah called for "Muslims all around the world" to kill 1,000 people for each of the dead imams, naming acceptable targets as "France, Italy, Denmark, Britain, Qatar and the United Arab Emirates."
With rebel forces claiming to be only 10 kilometres from Zliten, their next main military target on the road to Tripoli, their leadership also advanced on the diplomatic front.
US national security advisor Tom Donilon told Jibril "that the United States views the (National Transitional Council) as a legitimate and credible interlocutor of the Libyan people," the White House said.
Officials did not say whether Obama dropped by the meeting.
There was no immediate sign of new US financial help for the cash-strapped rebels. But the White House said it was working with Congress on changes to the law to allow a portion of around $30 billion in Qaddafi regime assets blocked in the United States to be funneled towards the opposition.
French President Nicolas Sarkozy will meet Jibril in Paris on Saturday, the French presidency said.
The Libyan opposition, based in the eastern city of Benghazi, wants Washington to recognise the body as "the sole" legitimate interlocutor of the Libyan people, he said.
Unlike France, Gambia, Italy and Qatar, the United States has not fully recognised the NTC. And White House spokesman Jay Carney said such a step was "premature."
NATO Secretary General Anders Fogh Rasmussen also was at the White House Friday for closed-door discussions with Obama.
Rasmussen said NATO was fulfilling its UN-mandated mission in Libya, had saved "numerous lives" and had stopped the Qaddafi regime's bid to retake the country by force after widespread uprisings.
In The Hague, ICC prosecutor Luis Moreno-Ocampo said he will seek arrest warrants for three people considered most responsible for crimes against humanity in Libya. His office wouldn't reveal the names, but diplomats expect Qaddafi is among them.
Moreno-Ocampo said he was also investigating the deaths of dozens of sub-Saharan Africans in Benghazi by an "angry mob" who believed they were Qaddafi mercenaries.
In Geneva, the UN refugee agency said it feared that up to 1,200 people fleeing Libya had died in the Mediterranean Sea so far and that it had found evidence that a military vessel refused to rescue one boat.
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