Following the strikes, dozens of Gadhafi supporters climbed atop the ruins, chanting support for their leader.
A building that housed a library, office and reception hall for visiting dignitaries was destroyed. Four people reportedly were injured.
It's not known where Gadhafi was at the time of the bombings.
The NATO strike came after Gadhafi's forces launched a deadly attack on the rebel city of Misrata. The shelling killed at least 32 people.
The battle for Misrata, which has claimed hundreds of lives in the past two months, has become the focal point of Libya's armed rebellion against Gadhafi since fighting elsewhere is deadlocked.
NATO's mandate from the U.N. is to try to protect civilians in Libya, split into a rebel-run east and a western area that remains largely under Gadhafi's control. While the coalition's airstrikes have delivered heavy blows to Gadhafi's army, they have not halted attacks on Misrata.
The Associated Press contributed to this report.