A NATO air strike has killed the Libyan leader's youngest son Saif al-Arab Gaddafi, a Libyan government spokesman has said.
Three of Muammar Gaddafi's grandsons were also killed in the strike on the residential villa in Tripoli, the spokesman said.
The spokesman said Colonel Gaddafi was in the same house but was unharmed.
The Libyan government said the air strike was a direct operation to assassinate the leader.
A NATO official said one of its air strikes hit a command centre in the Bab al-Azizya area of Tripoli, where Colonel Gaddafi's compound is located, but said its attacks aim for military targets, not individuals.
The official said the military alliance was aware of unconfirmed media reports that members of Colonel Gaddafi's family had been killed and it regretted any loss of life.
Libyan officials took journalists to the house, which had been hit by at least three missiles.
Reuters reports that some parts of the roof had caved in, leaving strings of reinforcing steel hanging down among chunks of concrete, the agency said.
Saif al-Arab Gaddafi, 29, was the youngest of Muammar Gaddafi's six sons.
Government spokesman Mussa Ibrahim said Saif al-Arab was a civilian and a student who had studied in Germany.
An international coalition began bombarding Libya on 19 March to enforce a UN Security Council resolution that set up a no-fly zone over the country and authorised the use of "all necessary measures" to protect civilians.
Colonel Gaddafi is fighting an uprising by rebels who have seized much of the eastern part of the country.
He had appeared on television in the early hours of Saturday, offering talks to the rebels and saying he would never step down. The insurgents rejected his proposal as hollow and treacherous.