Government officials said the NATO strikes were targeting the compound and other government buildings.
At the compound, there was a large hole in the ground near stairs leading to an underground passageway.
Libyan government spokesman Moussa Ibrahim said three people were killed in Thursday's strikes.
The strikes came hours after Gadhafi made his first TV appearance since an April 30 NATO attack on his compound that killed one of his sons.
NATO strikes earlier this week hit an intelligence building and another structure used by the government.
Intensified NATO airstrikes on Gadhafi's forces across Libya have given a boost to rebels fighting to oust the regime.
The rebels control most of eastern Libya, but the besieged port city of Misrata southeast of Tripoli is the only rebel stronghold in the west.
The Associated Press contributed to this report.