One air strike targeted a national security base east of the Jabalia refugee camp in the north of the strip, moderately injuring one Palestinian, medical sources said on Saturday.
Another air strike hit a base east of Gaza city in the Zeitoun neighbourhood while a third hit an empty field in the north of the Gaza Strip in Beit Hanoun.
Earlier on Friday, a rocket fired from the strip struck a parked bus in the town of Sderot without causing casualties, Israeli police said.
An Iron Dome anti-rocket battery also shot down a rocket over the southern city of Ashkelon.
A group called the Brigades of Omar Hadidi, which is believed to be affiliated with the Islamic State of Iraq and the Levant (ISIL), claimed responsibility on Twitter for firing the Grad rocket at Ashkelon.
The incidents came as violence between Palestinian protesters and Israeli security forces spread beyond the walls of Jerusalem's Old City on Friday, with at least eight Palestinians shot in clashes in the occupied West Bank and Israeli policemen injured by firebombs in a restive part of the city.
Hamas, which rules the Gaza Strip, had called for a "day of rage" over tensions at the city's Al-Aqsa Mosque compound.
The new wave of violence started on September 13 when Israeli police stormed Al-Aqsa Mosque compound to arrest whom they called Palestinian "stone throwers".