Israeli army bombardments have killed at least 33 people and struck 30 homes in the Gaza Strip, taking the death toll in the besieged enclave to more than 840 people.

Palestinian officials said on Friday that Israeli troops and Hamas fighters fought intense battles in the north and centre of the coastal strip, while the Israeli military announced it had hit 45 sites in Gaza.

One Israeli strike killed Salah Hassanein, a senior official from the Islamic Jihad group, and two of his sons, Al Jazeera’s correspondent reported.

Meanwhile, the Israeli army said that its missing soldier, Oron Shaul, had been killed in Gaza, in an attack on an APC on Sunday. Hamas claims to have taken him hostage, and his body has not been recovered. 

The army also said that another soldier was killed on Friday, putting the military death toll at 35. In addition, three Israeli civilians has been killed since the offensive started.

Earlier on Friday, Hamas’ armed wing fired three rockets towards Tel Aviv's Ben Gurion airport, an attack confirmed by Israel.

On Tuesday, a rocket landed near the international airport's runways, causing a two-day suspension of US and European flights to Tel Aviv. 

The Israeli offensive in Gaza has so far killed at least 848 Palestinians, including scores of children, and left more than 5,200 people injured.

Rockets fired from Gaza into Israel have killed two Israeli civilians and a Thai migrant worker. 

The leader of Lebanon's Hezbollah group, promised to support Palestinian fighters. In a live television appearance on Friday, Hassan Nasrallah warned Israel that it was "suicide'' to continue waging war in the Gaza Strip.

"We are true partners with this resistance ... their victory is all our victory, and their defeat is all our defeat," he said.

Diplomatic push

As casualties soared, high-level diplomatic efforts continued in an attempt to broker a ceasefire in Gaza.

The US secretary of state, John Kerry, met UN chief Ban Ki-moon in Cairo on Friday. Kerry also spoke by telephone to his Qatari and Turkish counterparts, who have influence with Hamas.

Efforts are focused on a week-long humanitarian ceasefire, during which intensive negotiations will tackle the blockade of Gaza and other disputes.

Hamas, which has fired hundreds of rockets at Israel during the Israeli offensive on Gaza, earlier rejected an Egyptian proposal.

The Palestinian group said any truce must include a guaranteed end to Israel's eight-year blockade on the Gaza Strip.

The Israeli paper Haaretz quoted a senior Israeli official as saying that Kerry had drafted a new ceasefire proposal and presented it to both sides.

Israel public radio reported that the country's security cabinet was expected to meet on Friday to discuss the proposal.

An unnamed senior Israeli source was quoted as saying: "If Hamas accepts the American proposal it is not impossible that there could be an Israeli decision to accept it also."

Source: Al Jazeera and agencies