There were no reported injuries in either incident on Monday after a two-day lull in violence that followed a bombing at an Israeli shopping mall on 5 December that killed five people.
The Israeli occupation army said a rocket slammed into the town of Sderot, near the Gaza border, but caused no damage or injuries.
Afterwards soldiers fired artillery at rocket launch sites in northern Gaza, Israeli military sources said.
Witnesses in Gaza City reported hearing 15 loud blasts from the exploding shells.
Members of the al-Aqsa Martyrs’ Brigades, a wing of the mainstream Fatah movement, said they carried out the rocket strike, saying it was a response to Israel’s killing of three of its members in air raids last week.