"The attack resulted in the martyrdom of brother Saif al-Arab Gaddafi (29) and three of the leader's grandchildren," official spokesperson Moussa Ibrahim told reporters in the wee hours.
"The house of Mr Saif al-Arab Gaddafi was attacked tonight with full power. The leader (Muammar Gaddafi) with his wife was there in the house with other friends and relatives," he said.
The spokesperson noted that the Libyan leader escaped unhurt.
"The leader himself is in good health, he wasn't harmed." Muammar Gaddafi's wife was also unharmed but other people in the house were injured.
"This was a direct attempt to assassinate the leader of the country."
According to reports, the building was extensively damaged and one unexploded bomb remains at the site. Saif al-Arab was the youngest of Gaddafi's six sons.
An international coalition began carrying out strikes on forces loyal to Gaddafi on March 19 under a UN resolution to protect civilians in Libya. NATO took over the operations on March 31.
Bouchard said he was aware of reports that some of Gaddafi's family members had been killed in the strike.
"We regret all loss of life, especially the innocent civilians being harmed as a result of the ongoing conflict," he said.
Saif al-Arab is the most unknown of the Libyan leader's children, Al Jazeera said. "He has been largely invisible since the conflict began" in February, it said.
"He hasn't been visible in any significant form. He hasn't appeared on TV or made any speeches, he hasn''t been on any crowd-rallying marches."
Ibrahim said Saif al-Arab had been studying in Germany. Libyan officials said Saif al-Arab's house had been hit by at least three missiles.
In a video broadcast by the satellite channel, Libyan officials showed reporters what they said was the destroyed house, a large crater, crumbled concrete and twisted metal.
In their reaction, rebels in Benghazi said they cannot trust Gaddafi. Al-Jazeera said there were "an awful lot" of suggestions in Libya's rebel-held eastern region that the news of the deaths could be fabricated.
One of the main spokesmen for the opposition Transitional National Council, Abdul Hafez Goga, said he thinks "it could all be fabrication, that it may well be Gaddafi is trying to garner some sympathy."
Three loud explosions were heard in Tripoli last evening as jets flew overhead. Volleys of anti-aircraft fire rang out following the first two strikes, which were followed by a third.
Earlier yesterday, NATO officials had rejected an offer by Gaddafi to call a ceasefire and negotiate as false.
The proposal was delivered in an often defiant speech by Gaddafi broadcast over Libyan state television, in which he asserted he would never leave Libya.
"Come France, Italy, UK, America, come, we'll negotiate with you," Gaddafi said. "You lie and say I'm killing my own people. Show us the bodies."