Israeli air strikes have killed the head of Islamic Jihad's rocket force in Gaza, part of an operation that has killed 25 people including women and children and been met with hundreds of rockets fired from the enclave.

Egypt was set to host senior Islamic Jihad official Mohammad al-Hindi in Cairo later on Thursday, part of mediation efforts to end the fighting, two Islamic Jihad officials and a foreign diplomat told Reuters.

Ali Ghali was the fourth senior Islamic Jihad commander killed since Israel began striking Gaza in pre-dawn raids on Tuesday.

The death toll in the raids includes at least five women and five children.

The military said Ghali had helped oversee the launch of rocket fire towards Israel in recent days as well as in previous rounds of fighting.

Islamic Jihad is an Iranian-backed militant group allied with Hamas, which rules the enclave.

Air raid sirens sounded in areas of southern Israel around the Gaza Strip, and Reuters images showed rockets intercepted by Israeli air defences in the night sky.

Israeli jets hit targets including a mortar post in the northern part of the enclave.

The Israeli military said it has attacked 158 targets in Gaza while at least 523 rockets were launched towards Israel this week, and 380 crossed into Israel but air defences intercepted 96 per cent of those that threatened to hit targets.

It also said more than 100 rockets had misfired, killing four Palestinians, including a 10-year-old girl, an assertion Islamic Jihad denied as "completely incorrect".

"Once again Israel tries to escape its responsibility for the killing of civilians through fabrications and lies," Islamic Jihad spokesman Dawoud Shehab said.

After more than a year of Israeli-Palestinian violence that has killed more than 100 Palestinians and at least 19 Israelis and foreigners since January, the latest escalation drew international alarm and calls for a ceasefire.

Egypt's foreign minister Sameh Shoukry and Jordanian Foreign Minister Ayman Safadi were also due to meet their French and German counterparts in Berlin later on Thursday to discuss peace efforts.

However, Israel rejected demands from Islamic Jihad that it end its policy of targeted killings of the group's leaders.

"We are not willing to accept delusional demands from the Islamic Jihad," said MK Yuli Edelstein, head of the Israeli parliament's Foreign Affairs and Defence Committee on Kan radio.

"Every now and then, we have to initiate action and this is exactly what the IDF and the Shin Bet (intelligence agency) did very successfully this time."

Both in blockaded Gaza, where residents have been experiencing decades of a worsening humanitarian crisis, and in Israeli towns nearby, schools and businesses remained closed as tension mounted over what might come next.

Israel has kept crossings for the movement of people and goods closed since Tuesday, stopping the entry of essentials such as food, fuel and humanitarian aid as well as the exit of patients who receive medical treatment outside the coastal enclave.

Israeli authorities estimated between 30 per cent and 60 per cent of communities living around Gaza have evacuated as a precaution.