Israel launched three successive airstrikes in central and southern Gaza overnight, in response to rocket and mortar fire from the coastal enclave, both sides reported Monday.
An Israeli army spokesman said three targets - a rocket launching site and two "terrorist" sites - were struck in one sortie at around midnight, dpa reported.
Witnesses said an unoccupied building under construction was destroyed in central Gaza, east of al-Bureij refugee camp near the border with Israel.
An empty field was also hit on Gaza City's southern outskirts, as was a training post of the Islamist Hamas movement in southern Gaza, east of Khan Younis. No injuries were reported.
The army spokesman said 11 rockets and mortar shells landed in Israel Monday after midnight, after Gaza militants fired another seven on Sunday, including at least one Russian-type Grad missile aimed at Beersheba, the largest city in the southern Israeli Negev desert.
It landed north of the city and caused no injuries, but schools were evacuated as a precaution.
The pro-Hamas Popular Resistance Committees said its militants fired Grad missiles.
Hamas' armed wing, the Qassam Brigades, said one of its members was killed and another seriously injured earlier Sunday in an Israeli airstrike in southern Gaza, as he was about to launch a rocket into Israel.
The renewal of the tit-for-tat violence between Israel and militant groups in Gaza came three days after the sides accepted an unofficial, Egyptian-brokered truce.
Ashraf al-Qedra, the spokesman of the Hamas-run Health Ministry in Gaza, said that since the latest round of violence erupted on October 22, Israel has killed nine Palestinian militants and wounded 14 others.
Israel said Gaza armed groups have launched more than 615 rockets and mortar shells at it this year.