In the most serious escalation in months, an Israeli missile attack on Tuesday also targeted the home of an Islamic Jihad official in Damascus, killing two people including one of his sons, Syrian state media says.

Islamic Jihad said the target was the home of political leader Akram al-Ajouri.

Hours later, sirens sounded in central Israeli cities, including the commercial capital of Tel Aviv the military and witnesses said, warning of possible rocket launches from the Gaza Strip.

Israel's home-front command ordered schools shut across southern and central Israel, and instructed civilians to stay at home and not go into work unless it was vital and public shelters were opened.

There were no immediate reports of casualties. Israeli media reported that some of the rockets were intercepted.

The slaying of Baha Abu al-Atta in his Gaza home looked likely to pose a new challenge for Gaza's ruling Hamas faction, which has mostly tried to maintain a truce with Israel since a 2014 war.

Israel said al-Atta had carried out a series of cross-border attacks and was planning more.

Israel casts rising Gaza tensions as part of a wider regional struggle with arch-foe Iran.

Al-Atta's wife was also killed in the blast that ripped through the building in Gaza City's Shejaia district before dawn, Islamic Jihad said. Two people were wounded.

Shortly after, Palestinian militants launched a salvo of rockets into Israel, setting off sirens as far as its port city of Ashdod, about 20km away, witnesses said.

Police closed roads on the Gaza outskirts as a precaution.

In a statement, the Israeli military said Netanyahu had authorised the operation against al-Atta, blaming him for recent rocket, drone and sniper attacks against Israel, and attempted infiltrations into the country.

"Abu Al-Atta was responsible for most of the Palestinian Islamic Jihad's activity in the Gaza Strip and was a ticking bomb," the statement said, accusing Al-Atta of planning "imminent terror attacks through various means".

An Islamic Jihad statement confirmed the death of Al-Atta, who it said had been in the midst of "heroic jihadist action".

"Our inevitable retaliation will rock the Zionist entity," the statement said, referring to Israel.

Syrian state media said the Israeli attack in Damascus had been carried out using several missiles, one of which was shot down over the nearby suburb of Daraya.

Syrian state media said six people were wounded in the attack, describing the target as a civilian home in Mezzah, a western district of the capital that is home to several foreign embassies.

Photos published by state news agency SANA showed damage to a two-storey building and debris strewn over cars.

Australian Associated Press