Israel's military has killed the head of the Palestinian Islamic Jihad (PIJ) rocket launching force in a pre-dawn air strike on an apartment in Gaza.

Two other people, who the military said were also militants, died in the attack in the southern city of Khan Younis.

Sirens later sounded in southern Israel as rockets and mortars were launched from Gaza. No injuries were reported.

On Wednesday, militants fired 507 rockets and mortars at Israel and Israel struck 158 PIJ targets in Gaza.

Twenty-five people have been killed and 76 injured in Gaza since Tuesday morning, when Israel began its operation against PIJ with a series of strikes that killed another three of its commanders, health officials there say.

At least 10 civilians are also among the dead, which the United Nations has called unacceptable.

The Israeli military said four people, including three children, were killed in Gaza by rockets falling short on Wednesday, though this has not been corroborated by Palestinian sources.

Islamic Jihad said the allegation was "completely incorrect" and accused Israel of trying to evade responsibility for their deaths.

There have been no fatalities in Israel, although several people have been injured while rushing to shelters, according to local health officials.

The early morning Israeli air strike in Khan Younis destroyed an apartment at the top of a six-storey building and damaged the apartment below it.

Abdullah Samir Hummaid, whose apartment in a neighbouring building was also damaged, said he had just got into bed when he saw "an extremely bright flash of light, turning the dark night into day, and then two explosions sounded within a few seconds".

"Stones and glass fell on us, we couldn't see a thing, and we didn't know where everybody was. I could hear the yelling and screaming of the children, and them calling out 'daddy, daddy'," he told Reuters news agency.

"I crawled to them, and found them covering their heads with their blankets," he added. "I took them and we went outside, I returned and took my wife and our six-month-old baby who had been hit by debris and glass."

The armed wing of the PIJ confirmed that the head of its missile unit, Ali Hassan Ghali, also known as Abu Mohammed, was killed the attack, which it described as a "treacherous Zionist assassination".

The Palestinian health ministry said three people were killed and seven others injured. Palestinian media reported that the two other dead were Ghali's brother and nephew.

The PIJ is the second biggest militant group in Gaza after Hamas, which controls the territory, and has been responsible for many of the rocket attacks on Israel in recent years.

The Israel Defense Forces (IDF) confirmed it had targeted Ghali and what it called two "other Islamic Jihad operatives in Gaza".

It described the commander as a central figure in the PIJ who had been "responsible for the recent rocket barrages launched against Israel".

Later on Thursday, militants in Gaza fired at least 10 mortars and five rockets at nearby Israeli communities in the southern Eshkol Regional Council, local officials said.

One of the rockets hit a chicken coop close to a home and caused extensive damage, they added.

Some of the rockets and mortars fired have hit homes and buildings, but most have landed in open areas or been intercepted.

Israel's Magen David Adom ambulance service said it had treated 32 people as of Thursday morning, 15 of whom were injured while running for shelters and 17 experienced severe anxiety, according to Israeli media.

The IDF said it struck a number targets belonging to PIJ as the rocket and mortar fire continued, including a command centre and an observation post.

On Wednesday night, Israeli Prime Minister Benjamin Netanyahu warned that Israel's campaign was not over.

"We have hit Islamic Jihad with the most significant blow it has ever suffered," he said, referring to the killing of the three PIJ commanders on Tuesday and the targeting of dozens of the group's rocket and mortar launch sites.

Islamic Jihad threatened dark days ahead if Israel "increased its aggression".

A spokeswoman for UN Secretary General António Guterres said that he was following with deep concern the developments in Gaza and "condemns the civilian loss of life, including that of children and women, which he views as unacceptable".

"The secretary general urges all parties concerned to exercise maximum restraint and to work to stop hostilities immediately," she added.

Egypt is working to try to secure a ceasefire between the two sides.

Israel's Foreign Minister, Eli Cohen, said on Wednesday that it was "assessing" a proposal from Cairo. Palestinian factions reportedly want Israel to agree to stop what it calls "targeted assassinations".

This week's fighting is the heaviest since three days of hostilities between Israel and PIJ last August, in which 49 Palestinians were killed in Gaza.

There was a serious flare-up last week, as PIJ and other groups fired more than 100 rockets into Israel over two days, following the death in an Israeli prison of a Palestinian hunger striker. The Israeli military carried out air strikes on sites it said were linked to Hamas in response.

Tensions also remained high in the occupied West Bank on Wednesday, after Israel carried out arrest raids.

Three Palestinians were killed in the town of Qabatiya by Israeli forces, who said the trio had fired at them. An Israeli soldier was also seriously wounded during a separate exchange of fire with Palestinian gunmen in Tubas.

Additional reporting by Antoinette Radford in London