Air strikes on Monday killed 10 Palestinians raising the toll to 87, as Israel pushed raids against Hamas into a sixth day amid a flurry of efforts to broker a truce.

The latest deaths, which medics and Palestinian security officials said occurred right across the Gaza Strip, came after a night of air strikes and sustained fire from navy ships which also levelled a police station.

As the violence escalated, international efforts to broker a ceasefire gathered pace, with senior Hamas officials in Cairo saying Egyptian-mediated talks on Sunday with Israel were "positive" but now focused on the need to guarantee the terms of any truce.

Egypt, led by President Mohamed Morsi, has been pressed to exert its influence on Gaza's Hamas rulers to restore calm.

Morsi's office said that the president had met with both Hamas chief Khaled Meshaal and Islamic Jihad chief Abdullah Shalah to discuss "Egyptian efforts to end the aggression."

UN leader Ban Ki-moon urged Israel and Hamas to work with Egypt to reach a ceasefire, and in a statement said he was heading for the region to support truce efforts.

His office did not say when he would arrive but Israel's foreign ministry said it was expecting him on Wednesday, with the Palestinians also confirming he would meet Palestinian president Mahmud Abbas at some point.

Palestinian officials said it was possible a deal would be reached as early as Monday, despite warnings by Israel it was gearing up to expand its operation, which until now has been predominantly an air campaign, into ground offensive.

Analysts say Israel's leadership appears satisfied with the success of Operation Pillar of Defence, which it launched on Wednesday aimed at halting Palestinian rocket fire, and that could it be ready for a ceasefire.

But Hamas, emboldened by Arab support, has demanded as conditions for a ceasefire that Israel lift its siege of Gaza, in place since 2006, and international guarantees that it will halt attacks on Gaza, including assassinations of the movement’s leaders.

The latest operation against the Gaza Strip began with the targeted killing of Hamas military chief Ahmed Jaabari in an air strike in Gaza City on Wednesday.

Israel's Foreign Minister Avigdor Lieberman insisted that "the first and absolute condition for a truce is stopping all fire from Gaza," and that all armed groups would have to commit to it.

The Israeli army said on Monday morning it had "at least 80 terror sites" overnight, including the Hamas police headquarters, bringing the number of sites it has targeted in Gaza to more than 1,350.

A military spokeswoman said no rockets from Gaza hit Israel overnight, although at least two exploded in the early hours of Monday.

Among those killed on Monday were three farmers killed in two separate air strikes, as well as three members of the same family who died in a strike on a car in Deir al-Balah in central Gaza, Palestinian officials said.

In Gaza City, two women and a child were among four killed in a strike on the Zeitun neighbourhood.

Monday's deaths came after multiple raids on Sunday that killed 29, in the bloodiest day of Israel's bombing campaign. Three Israelis have been killed and more than 50 injured by rocket fire since Wednesday.

By far the deadliest strike on Sunday was in northern Gaza City where a missile levelled a three-storey building, killing nine members of the Al-Dallu family -- five of them children -- and two of their neighbours, medics said.

Prime Minister Benjamin Netanyahu warned on Sunday that Israel was ready to "significantly expand" its operation as public radio reported that 40,000 reservists were amassed near the Gaza border, ready for a ground incursion.

US President Barack Obama said it was "preferable" for the Gaza crisis to be resolved without a "ramping up" of Israeli military activity, while French Foreign Minister Laurent Fabius said his country was willing to help broker a truce.

British Foreign Secretary William Hague said "a ground invasion of Gaza would lose Israel a lot of the international support and sympathy that they have in this situation."