The attacks that came early on Sunday also targeted the office of a pro-Hamas newspaper.
The first attack wounded several bystanders on the ground below, including two children, but there were no immediate reports of casualties in the second strike.
Israeli army said the first office was used by al-Aqsa Martyrs Brigades, a Palestinian resistance group within Arafat's Fatah movement, to plan attacks against Israel.
Palestinian witnesses said the office belonged to Fatah's political faction and not resistance fighters.
The second strike hit the office of a pro-Hamas newspaper, al-Risala. The Israelis claimed the paper was used to "incite terror and to pass messages of the Hamas leadership."
"We attacked two structures used for terror activity," said an Israeli army spokesman.
The latest air strikes came just a day after Israeli helicopters targeted buildings in the Gaza in a failed attempt to assassinate two senior Islamic Jihad leaders.
The Israeli army later said the air strikes were successful in destroying an explosives lab.
Israel is under pressure to withdraw from the occupied Gaza Strip, where 7500 hard line Jewish settlers live in hard-to-defend settlements amid 1.3 million mostly impoverished Palestinians.
A rally urging a withdrawal drew a crowd of more than 100,000 Israelis in Tel Aviv on Saturday night.