Earlier, forces loyal to Libyan leader Colonel Muammar Gaddafi attacked the rebel stronghold of Benghazi despite declaring a ceasefire a day earlier.
Western planes bombed targets in the capital, Tripoli, said the AFP news agency, quoting witnesses and state TV.
A French plane fired the first shots at 1645 GMT, destroying Libyan military vehicles, according to a military spokesman.
UK Prime Minister David Cameron has confirmed that British planes are in action over Libya.
He repeated that no US ground troops would take part.
Shortly after the bombing started, a Libyan official went on TV to denounce the "barbarian aggression".
A British submarine has fired a number of missiles at Libyan air defence targets, the Ministry of Defence said.
Mr Cameron said that launching military action against Libya was "necessary, legal and right".
Libyan state TV reported that what it called the "crusader enemy" had bombed civilian areas of Tripoli, as well as fuel storage tanks supplying the western city of Misrata.
Sources in Tripoli told BBC Arabic that the attacks on the city had so far targeted the eastern areas of Sawani, Airport Road, and Ghasheer. These are all areas believed to host military bases.
The action came hours after Western and Arab leaders met in Paris to agree how to enforce the UN resolution, which allows "all necessary measures" to protect civilians from forces loyal to Col Gaddafi.
French planes also flew reconnaissance missions over "all Libyan territory", military sources in Paris said earlier.
Canada is also sending warplanes to the region, while Italy has offered the use of its military bases. A naval blockade against Libya is also being put in place.
The international community was intervening to stop the "murderous madness" of Col Gaddafi, French President Nicolas Sarkozy said.
"In Libya, the civilian population, which is demanding nothing more than the right to choose their own destiny, is in mortal danger," he warned. "It is our duty to respond to their anguished appeal."
Col Gaddafi has ruled Libya for more than 40 years. An uprising against him began last month after long-time leaders of neighbouring Tunisia and Egypt were toppled.
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