Three bombs were dropped near Bab Al-Aziziya, which houses a command and control centre, Nato officials said. The second strike hit an army barracks, the AFP news agency says.
The series of blasts have caused the collapse of parts of walls around the barracks, which is full of warehouses, although the Libyan authorities say they have been emptied.
Nato officials say the target of two or three bombs was a vehicle storage area in Bab Al-Aziziya.
The strikes came after US President Barack Obama’s promise to “finish the job” in Libya at the Deauville G8 summit in Friday and Russia joined explicit calls for Kadhafi to go.
Elsewhere, rebels fought Kadhafi loyalists near an oil facility in the eastern town of Ajdabiya, leaving two of the insurgents dead, rebel commander Jamal Mansur told AFP.
There were also sporadic clashes around the rebel-held southern oasis town of Jalo, as Kadhafi's forces tried to seize oil and gas reserves.
Following a Russian offer to mediate the Kadhafi regime said any initiative to resolve the crisis would have to go through the African Union, which on Thursday called for an end to the Nato strikes.
"The G8 is an economic summit. We are not concerned by its decisions," said Libya's Deputy Foreign Minister, Khaled Kaaim.
Kaaim confirmed that South African President Jacob Zuma will visit Tripoli on Monday, without indicating whether Kadhafi's exit would be discussed as the South Africans have claimed.