Seif al-Arab Gadhafi was the sixth son of Gadhafi and brother of the better known Seif al-Islam Gadhafi. The younger Gadhafi had spent much of his time in Germany in recent years.
Moammar Gadhafi and his wife were in the Tripoli house of Seif al-Arab Gadhafi, 29, when it was hit by at least one bomb dropped from a NATO warplane, according to Libyan spokesman Moussa Ibrahim.
"The leader himself is in good health," Ibrahim said. "He was not harmed. The wife is also in good health."
Rebel forces fired their guns in the air to celebrate the strike on Gadhafi.
NATO rejected Moammar Gadhafi's call for a cease fire and negotiations earlier Saturday, saying they need actions not words.
Gadhafi called for the cease fire and negotiations with NATO powers in a live pre-dawn speech on Saturday.
"The door to peace is open," Gadhafi said, sitting behind a desk. "You are the aggressors. We will negotiate with you. Come, France, Italy, U.K., America, come, we will negotiate with you. Why are you attacking us?"
However, a NATO official said Gadhafi's forces must end their attacks on civilians before the offer will be considered.
According to the official, Gadhafi's regime has announced cease fires several times before and continued attacking cities and civilians.
Meantime, aid ships were prevented from docking in a besieged coastal city while the alliance swept the port for mines.
Human Rights Watch said two mines had been destroyed by NATO forces combing the Misrata port while a third was being closely monitored. The alliance did not give details but said the process would take time.
NATO also bombed a government complex that included the state television building in Tripoli. The Libyans alleged the strike was meant to kill Gadhafi as his address was broadcast live on state TV, but the TV building was not damaged and Gadhafi spoke from an undisclosed location.
Torrance resident Iman Traina, who just returned from Libya, said the violence is getting worse by the day.
"There was a girl in the outskirts of our city that was raped and sodomized at the age of 6 by the regime forces," Traina said. "It's in complete, horrible humanitarian conditions."
"Finally Gadhafi is tasting with his own family what he was doing to all families inside Libya," said Traina's father, Idris Traina.
The Associated Press contributed to this report.
