Witnesses say Israeli warplanes destroyed the Palestinian Foreign Ministry building in Gaza City early Monday.
The strike damaged homes in the area, and several injuries were reported.
Israel bombed the same building last week, saying it has been used to plan terror attacks against the Jewish state. The building housed the offices of Palestinian Foreign Minister Mahmoud Zahar, a leader of the Hamas-led Palestinian government.
On Sunday, Israeli troops killed five Palestinian militants and one civilian during new military operations in the Gaza Strip.
Palestinian witnesses said several others were injured in the strikes. An Israeli airstrike also hit a vehicle carrying militants in the town of Beit Hanoun, but witnesses said the men were unharmed.
Israel's military ordered troops to return to Gaza in an effort to stop Palestinian missile attacks and retrieve a kidnapped Israeli soldier.
Israel started its offensive in Gaza on June 28, three days after Palestinian militants captured an Israeli soldier and killed two others. Israel said it intends to secure the release of the captured soldier and stop Palestinian rocket fire.
Some information for this report was provided by AP and Reuters.