Moussa Ibrahim, the government spokesman, said Gadhafi and his wife were not harmed, although they were at the house at the time, The New York Times reported. Ibrahim said Seif al-Arab Moammar el-Gadhafi was killed.
The airstrike came hours after Gadhafi delivered a defiant 80-minute television address. He called on Libyan rebels to agree to a cease-fire and said he would not step down.
Both rebel leaders and NATO officials rejected Gadhafi's demands.
In Benghazi, the rebel's de facto capital, celebratory gunshots could be heard early Sunday, the Times said. Ibrahim in his statement blasted the rebels and NATO.
"Tonight and only a short time ago, the Western crusader aggression against the Libyan nation continued and proved again that it has no moral foundation, no legal foundation and no political foundation," he said.
Earlier Saturday, NATO officials said Gadhafi's troops would have to return to their bases and the regime would have to allow complete access by aid groups, the BBC reported.
"Gadhafi's regime has lost all credibility," Abdul Hafiz Ghoga, vice chairman of the Transitional National Council, said in a statement. "The time for compromise has passed. The people of Libya cannot possibly envisage or accept a future Libya in which Col. Gadhafi's regime plays any role."
Gadhafi spoke Saturday morning in a speech broadcast from Tripoli.
"I'm not leaving my country," he said. "No one can force me to leave my country and no one can tell me not to fight for my country."
Gadhafi's armed response to demonstrations calling for democratic reform led the U.N. Security Council to authorize NATO forces to protect Libyan civilians from Gadhafi's military.
"We will not surrender, but I call on you to negotiate," Gadhafi said. "Between Libyans, we can solve our problems without being attacked, so pull back your fleets and your planes."
Gadhafi alleged the rebels who took up arms in mid-February were "terrorists who are not from Libya, but from Algeria, Egypt, Tunisia and Afghanistan," the BBC reported.