Some of the strikes appear to have targeted Libyan leader Col Muammar Gaddafi's Bab al-Aziziya compound.
They came after France announced it and the UK would also deploy attack helicopters to escalate strike power.
Nato is enforcing a UN resolution to protect civilians, following the uprising against Col Gaddafi's rule.
Between 12 and 20 explosions were reported in the early hours of May 24.
The BBC's Andrew North, in Tripoli, said the first blasts were in the vicinity of Bab al-Aziziya and were followed by more in other parts of the city.
He says the hotel journalists have been staying in was shaken to its foundation by some of the blasts.
After each a Nato aircraft could be heard in the sky.
Plumes of smoke were rising from the area of Bab al-Aziziya and anti-aircraft guns were firing.
Libyan government spokesman Moussa Ibrahim said three people were killed and 150 wounded in the strikes.
Mr Ibrahim said barracks of a volunteer unit of the Libyan army had been targeted but most of the casualties were civilians living nearby. The statements could not be independently verified.
Our correspondent says he has not been taken to the barracks but was escorted to a hospital and shown people said to have been injured in the strikes.
He says people have come out on to the streets to show support for Col Gaddafi.
The attacks came after French Defence Minister Gerard Longuet confirmed media reports that France was deploying attack helicopters to Nato's Libya mission.
He also said Britain would send helicopters. He said both countries would deploy the new forces as soon as possible.
The UK has yet to confirm the deployment.
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