Israel has rejected a US-initiated proposal for a full truce in the Gaza Strip, but says it is considering a 12-hour humanitarian ceasefire to its campaign, which has killed hundreds of Gazans.

Israel TV reported on Friday that the country's security cabinet had rejected a US-initiated proposal in its current form, as it would end an ongoing effort to destroy Hamas tunnels under the Gaza-Israel border.

It was later reported by news agencies and Israeli media that Israel was however considering a 12-hour humanitarian ceasefire on Saturday, which would end bombardment at 4am GMT on Saturday, but not operations against the tunnels.

The Reuters news agency quoted a US official as saying that the Israeli prime minister, Benjamin Netanyahu, had discussed the 12-hour pause with the US secretary of state, John Kerry.

The full US proposal, which was being drawn up in Cairo, called for a week-long pause in fighting over the Muslim holiday of Eid. During that time, Hamas and Israel would begin indirect talks on easing Gaza blockade.

Hamas has previously said any truce must include a guaranteed end to Israel's eight-year siege of the enclave, while Israel has said it would reject any deal that included such a plan.

At a news conference in Egypt, the US secretary of state, John Kerry, confirmed the rejection but said diplomats were still trying to agree a deal.

"We still have terminology and context to work through, but we are confident we have a framework that will work, and we will continue to work for that ... none of us here are stopping."

Kerry met UN chief Ban Ki-moon in Cairo on Friday, and spoke by telephone to his Qatari and Turkish counterparts, who have influence with Hamas. Kerry will fly to Paris on Saturday for another conference on Gaza.

More deaths as diplomacy stutters

The Israeli offensive on Gaza has continued on Friday on its 18th day, with dozens of Palestinians reported dead.

The Israeli army said that its missing soldier, Oron Shaul, had been killed in Gaza. Hamas claimed to have taken him hostage on Sunday, and his body has not been recovered.

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

Rockets fired from Gaza into Israel have killed two Israeli civilians and a Thai migrant worker. A total of 35 Israeli soldiers have died in Gaza.

Meanwhile, 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.