"Following Hamas' constant rocket firing, the Israel Defence Forces will now resume their aerial, naval and ground activity in the Gaza Strip," the official said.
Israel's security cabinet approved a 24-hour extension Saturday night to a UN-brokered 12-hour humanitarian cdeasefire in Gaza.
But Islamic Hamas movement Sunday said any truce that does not guarantee a complete withdrawal of Israeli forces from the Gaza Strip will not be accepted.
"Any humanitarian ceasefire that doesn't secure the withdrawal of occupation soldiers from inside Gaza's borders, allow citizens back into homes, and secure the evacuation of the injured is unacceptable," Hamas spokesman Sami Abu Zuhri said.
The rocket fire from Gaza was resumed Saturday night in southern and central Israel, and has continued Sunday.
According to the Israeli military, overall, 25 rockets were fired at Israel since Saturday night.
One Israeli soldier was killed during the temporary ceasefire Saturday near the Gaza-Israel border after he was hit by a mortar shell fired from Gaza.
The ongoing fighting between the Hamas movement and the Israeli army in Gaza, which started in July 8, has claimed the lives of more than 1,000 Palestinians.
On the Israeli side, 46 people were killed, 43 of them were soldiers.