The house of Seif al-Arab Qaddafi, 29, "was attacked tonight with full power," government spokesman Moussa Ibrahim told a news conference announcing the deaths in the Saturday evening strikes.
"The leader himself is in good health; he wasn't harmed. His wife is also in good health; she wasn't harmed, (but) other people were injured," he added.
Mr. Ibrahim later said intelligence on Qaddafi's whereabouts seemed to have been "leaked."
"They knew about him being there, or expected him for some reason," the spokesman said.
NATO denied it was not targeting Colonel Qaddafi or his family but said it had carried out an airstrike on a military post in Tripoli.
"NATO continued its precision strikes against regime military installations in Tripoli overnight, including striking a known command and control building in the Bab al-Aziziyah neighborhood shortly after 18:00 GMT Saturday evening," the alliance said in a statement.
"All NATO's targets are military in nature ... We do not target individuals," he said in a statement.
Mr. Saif al-Arabis one of ColonelQaddafi's less prominent sons, with a limited role in the power structure. Ibrahim described him as a student who had studied in Germany.
The grandchildren killed were pre-teens, Mr. Ibrahim said.
The appearance of an assassination attempt against Gaddafi is likely to lead to accusations that the British- and French-led strikes are overstepping the UN mandate to protect civilians.
"I am aware of unconfirmed media reports that some of Mr. Qaddafi's family members may have been killed," said Mr. Bouchard. "We regret all loss of life."
Colonel Qaddafi had called for talks on a ceasefire, but NATO and the Libyan Transitional Opposition Council dismissed the call and insisted that Mr. Qaddafi cease attacks on civilians first.
Colonel Qaddafi said in his speech that NATO “must abandon all hope of the departure of Muammar Qaddafi. I have no official functions to give up: I will not leave my country and will fight to the death.”
The speech was billed as one marking the centenary of a battle against Italian occupation forces. Contemporary Italy is part of a NATO military campaign against Colonel Qaddafi’s forces.
“We are ready to talk with France and the United States, but with no preconditions,” Mr. Qaddafi said.
“We will not surrender, but I call on you to negotiate. If you want petrol, we will sign contracts with your companies—it is not worth going to war over,” Colonel Qaddafi said. “Between Libyans, we can solve our problems without being attacked, so pull back your fleets and your planes.”
The regime has announced ceasefires several times before and continued attacking cities and civilians ... Any ceasefire must be credible and verifiable,” a NATO official told Reuters.
Weeks of NATO air strikes have failed to dislodge the Libyan leader, but have instead created a stalemate on a war Colonel Qaddafi initially looked to have been winning. But the military situation is fluid now, with government forces held at bay in the east and around the besieged city of Misrata, while fighting rebels for control of the western mountains.
(Mustapha Ajbaili of Al Arabiya can be reached at: Mustapha.firstname.lastname@example.org)