Israeli air strikes have killed 31 Palestinians in the bloodiest day so far of its air campaign on the Gaza Strip, as diplomatic efforts to broker a truce intensified.

With Egypt at the centre of efforts to broker a ceasefire, Palestinian officials said it was possible a deal would be reached “today or tomorrow’’.

But there was no let-up in the bloodshed in the Hamas-run Gaza Strip. Medics said women and children accounted for most of yesterday’s dead, among them five babies and toddlers, killed in yesterday’s Israeli air strikes.

In the day’s most lethal raid, at least nine members of the same family — five of them children — were among 10 people killed when an Israeli missile destroyed a family home in Gaza City, the Health Ministry said.

At the scene, medics and bystanders all pitched in to remove the rubble to dig out the bodies in the hope of finding survivors, as people watched in shock, some weeping openly.

The latest violence hiked the Palestinian casualty toll to 77 dead and 700 injured in some 100 hours of raids, while three Israelis have been killed and more than 50 injured by rocket fire since Wednesday.

An Israeli air strike in the early hours of today morning levelled the Abbas police headquarters in Gaza City, but nobody was killed.

With Israel warning it could further escalate its operations in Gaza, US President Barack Obama had yesterday said it was “preferable” for the Gaza crisis to be resolved without a “ramping up” of Israeli military activity.

In Cairo, senior Hamas officials said Egyptian-mediated talks with Israel to end the bloodshed were “positive” but now focused on the possible stumbling block of guaranteeing the terms of a truce.

An outcome acceptable to Hamas would involve assurances about the United States, Israel’s main backer, being the “guaranteeing party,” one official said on condition of anonymity.

Security officials in Cairo said an Israeli envoy had also arrived in the Egyptian capital yesterday for the talks.

Egypt’s President Muhammad Mursi, meanwhile, met with both Hamas chief Khaled Meshaal and Islamic Jihad chief Abdullah Shalah to discuss “Egyptian efforts to end the aggression,” his office said without giving details.

But 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.