GAZA CITY - Israeli warplanes struck the Gaza Strip on Wednesday after the first rocket fire from the Palestinian territory in weeks hit an Israeli city, in a blow to efforts to avert a new war.

Gaza's rulers Hamas disavowed the rocket fire, saying they rejected "all irresponsible attempts" to undermine Egyptian efforts to broker a new long-term truce.

But Israel, which holds Hamas responsible for all rocket fire from the territory regardless of who launches it, struck 20 targets in Gaza, killing one Palestinian, according to the Hamas-run health ministry.

Israel also closed both its border crossings with Gaza in reprisal, further isolating the blockaded enclave where deteriorating living conditions have stoked violent protests along the border.

Gaza militants fired two rockets before dawn, one of which caused major damage to a family home in the southern city of Beersheba, 40 kilometres (25 miles) away, the Israeli army said.

The family of three children narrowly escaped injury after their mother moved them into the safe room, with much of the rest of the house destroyed, the army said.

ICC prosecutor 'keeping close eye' on Gaza violence

The International Criminal Court's chief prosecutor warned Wednesday she was keeping a "close eye" on the situation in the volatile Gaza Strip and would not hesitate to act if necessary.

Fatou Bensouda's warning comes after Israeli warplanes pounded Palestinian targets in the wake of a rocket attack early Wednesday - the first such incident in weeks. The ICC launched a preliminary probe in 2015 into allegations of war crimes and crimes against humanity in Israel and the Palestinian territories, in the wake of the Gaza war.

Bensouda said in a statement from The Hague-based court that she was "alarmed by the continued violence, perpetrated by actors on both sides, at the Gaza border with Israel." "As prosecutor seized of the situation in Palestine, I therefore feel compelled to remind all parties that the situation remains under preliminary examination by my office," she added.

"I continue to keep a close eye on the developments on the ground and will not hesitate to take any appropriate action."

Despite a visit to the region, the ICC has yet to move to the next stage and open a full-blown investigation which could possibly lead to charges being brought.

The issue is highly sensitive, with White House National Security Advisor John Bolton in September having threatened to arrest ICC judges if they moved against Israel or the United States.

Neither Israel or the United States are members of the ICC, which was set up in 2002 to probe the world's worst crimes including war crimes and crimes against humanities.

Gaza's Islamist rulers Hamas have disavowed the latest rocket fire saying they rejected "all irresponsible attempts" to undermine Egyptian efforts to broker a new long-term truce.

But Israel, which holds Hamas responsible for all rocket fire from the territory regardless of who launches it, struck 20 targets in Gaza, killing one Palestinian, according to the Hamas-run health ministry.

Israel also closed both its border crossings with Gaza in reprisal, further isolating the blockaded enclave where deteriorating living conditions have stoked violent protests along the border.