Missiles struck the Tripoli residence of Gaddafi’s most low profile son which the Libyan leader was visiting at 8 p.m. Saturday, causing extensive damage, media reports said.
Libyan government spokesman Mossa Ibrahim said the raid — the roaring explosion was heard in a large area — killed al-Arab Gaddafi, 29, and the three grandchildren.
The Libyan leader and his wife were in good health, he said, accusing the NATO of trying to assassinate Gaddafi in violation of international law.
The three-storey building in Bab al-Azizya neighbourhood was partially destroyed.
A part of the roof caved in, leaving mangled rods of reinforcing steel hanging down among splintered chunks of concrete, Xinhua reported.
When a Xinhua reporter visited the site, no bodies were to be seen.
Libyan officials said three missiles hit the house. Two exploded while the third lay in one of the rooms.
The air strike sparked mass protests on the streets in Libya, which Gaddafi continues to control despite a revolt against his leadership that has led to a part of his country falling into rebel hands.
NATO said it did stage airstrikes on Tripoli but would not confirm the Libyan claim about the deaths and the assassination attempt.
"NATO continued its precision strikes against Gaddafi 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," NATO said in a statement.
The alliance insisted all its targets were military in nature and linked to Gadhafi’s "systematic attacks on the population".
The commander of the NATO operation, Lt Gen Charles Bouchard, said he was aware of unconfirmed reports that some Gadhafi family members may have been killed and he regretted "all loss of life".
On Saturday, Gaddafi called for a ceasefire and negotiations in a televised speech but said a dialogue could take place only if NATO halted its airstrikes.
But Gaddaffi also said: "We are already in a war with Italy since Italians kill our children in 2011 as they did in 1911, that is why I cannot forbid Libyans to defend their lives and carry the military actions on the enemy’s territory."
Italy is one of 14 NATO members that contribute troops to the alliance’s military operation in Libya.
Italy said last Monday it would expand its role in the operation by authorising airstrikes on Gaddafi’s ground forces.
A total of 14 of the 28 NATO countries are taking part in the operation Unified Protector in Libya, which includes air strikes, a no-fly zone and naval enforcement of an arms embargo.
The UN Security Council adopted a resolution imposing a no-fly zone over Libya March 17, paving the way for a military operation against Gaddafi which began two days later.
The command of the operation was shifted from a US-led international coalition to NATO in late March.