Mussa Ibrahim said Saif al-Arab was a civilian and a student who had studied in Germany. He was 29 years old.
"The leader himself is in good health," Ibrahim said. "He was not harmed. The wife is also in good health."
"The attack resulted in the martyrdom of brother Seif al-Arab Gadhafi, 29 years old, and three of the leader's grandchildren," the government spokesman said. Seif al-Arab "was playing and talking with his father and mother and his nieces and nephews and other visitors when he was attacked for no crimes committed."
"What we have now is the law of the jungle," Ibrahim told a news conference. "We think now it is clear to everyone that what is happening in Libya has nothing to do with the protection of civilians."
Libyan officials took journalists to the house, which had been hit by at least three missiles. The roof had completely caved in in some areas, leaving strings of reinforcing steel hanging down among chunks of concrete.
A table football machine stood outside in the garden of the house, which was in a wealthy residential area of Tripoli.
Sunday morning saw NATO deny targeting members of Muammar Gadhafi's family: "NATO continued its precision strikes against regime military installations in Tripoli overnight, including striking a known command and control building in the Bab al-Azizya neighborhood shortly after 1800 GMT Saturday evening," a NATO statement said.
NATO's commander of Libya operations, Canadian Lieutenant-General Charles Bouchard, said the target was part of a strategy to damage Gadhafi's ability to plan and conduct attacks on civilians:
"All NATO's targets are military in nature and have been clearly linked to the Gaddafi regime's systematic attacks on the Libyan population ... We do not target individuals.
"I am aware of unconfirmed media reports that some of Gadhafi's family members may have been killed," he said. "We regret all loss of life, especially the innocent civilians being harmed as a result of the ongoing conflict."
Celebrations in Benghazi
Meanwhile, celebrations erupted in the rebel stronghold of Benghazi following the announcement that Gaddafi’s son was killed. Residents poured into the streets as celebratory gunshots and explosions could be heard in the city.
Gaddafi, who seized power in a 1969 coup, is fighting an uprising by rebels who have seized much of the eastern part of the country. British and French-led NATO forces are permitted under a United Nations resolution to mount air attacks on Gaddafi forces to protect civilians.
Gaddafi had appeared on television in the early hours of Saturday and said he would never step down. He offered talks to the rebels, who rejected the proposal as hollow and treacherous.
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