U.N. Secretary-General Ban Ki-moon said he had authorized the strikes, accusing Gbagbo of using heavy weapons against Ivory Coast civilians and the U.N. forces trying to protect them.
Residents from nearby neighborhoods reported seeing two U.N. Mi-24 attack helicopters and a French helicopter open fire on the residence, where Gbagbo is holed up in a bunker. The residents couldn't be named for fear of reprisal.
An Associated Press reporter saw the helicopters take off from the French military base followed minutes later by explosions coming from the direction of the residence. Successive waves of French helicopters took off from the base in the following hours and additional bombardments could be heard.
Gbagbo has been living in a bunker in his residence in Abidjan for nearly a week. After a decade in power, he refuses to step aside even though the United Nations has ruled that he lost the November presidential election to Alassane Ouattara.
Forces loyal to Gbagbo were encircled at the presidential residence earlier this week but broke out on Saturday, ambushing a patrol of soldiers loyal to his rival and advancing downtown.
Pro-Gbagbo forces also attacked U.N. headquarters on Saturday and again on Sunday.
In New York, a statement issued by the U.N. secretary-general accused Gbagbo and supporters of saying earlier in April that they were willing to negotiate an end to the crisis but that "they, in fact, used that time to regroup their forces and redeploy heavy weapons."
Since then, Ban said, Gbagbo's forces have attacked U.N. peacekeepers, civilians and the Golf Hotel where Ouattara is holed up.
Ban said he authorized U.N. units, with backing from French forces, to carry out attacks aimed at eliminating Gbagbo's heavy weapons.
He urged Gbagbo again "to step aside immediately" and turn the government over to Ouattara.
In Ivory Coast, U.N. spokesman Hamadoun Toure said: "This is in retaliation for a series of attacks for the last three or four days not only against (the U.N.) but also against the civilian population – often with heavy weapons."
Toure said Sunday's airstrikes targeted the presidential palace and Gbagbo's residence, as well as military bases where heavy weapons had been identified.
Gbagbo has lost control of virtually the entire country in the last two weeks as forces loyal to Ouattara have swept down from the north and west into the commercial capital. U.N. and French forces joined the effort last week, and a first round of U.N. and French airstrikes destroyed much of his arsenal of tanks, mortars and other heavy weapons.
In the wake of the onslaught, Gbagbo and his top military men were negotiating a surrender early last week that had raised expectations the four-month political standoff was nearing an end. But he continued to assert he would not give up power and was the legitimate president of Ivory Coast.
"I am concluding that Mr. Gbagbo has lost contact with reality," said the U.N. peacekeeping mission head, Choi Young-jin.
The United Nations said the Golf Hotel in Abidjan where Ouattara is based came under attack late Saturday and one peacekeeper was injured. Rockets and mortars landed on the hotel grounds shortly after U.N. forces came under attack nearby, said U.N. spokesman Toure. One peacekeeper was evacuated to a hospital with serious injuries, he said.
Massere Toure, a communications adviser for Ouattara, denied the hotel itself was targeted by the attack, which she said started when a patrol sent out from the hotel was ambushed by forces loyal to Gbagbo. Toure confirmed that stray bullets and at least one mortar landed on hotel grounds during the fighting.
Ouattara's forces have repeatedly said they do not want to kill Gbagbo, a move that would stoke the rage of supporters of the strongman, who won 46 percent of the vote in last year's election.
