Violence reverberated across Gaza on Monday with four Palestinians killed in Israeli air strikes as Egypt proposed a new ceasefire that would open key crossings into the blockaded territory.

Since an earlier ceasefire arrangement collapsed on August 19, the death toll in Gaza has risen steadily with 106 Palestinians killed in more than 350 Israeli air strikes across the territory.

Over the same period, more than 650 rockets have struck Israeli territory, one of which killed a four-year-old boy over the weekend, army figures show. Around 100 rockets were shot down.

Since midnight, Israeli strikes have killed four Palestinians, including two women and a three-year-old boy, raising the Gaza death toll to 2,124.

On the Israeli side, 68 people have been killed, the vast majority soldiers.

Another 38 rockets fired from Gaza struck the Israeli south on Sunday, while another was shot down, army statistics showed.

Prime Minister Benjamin Netanyahu said Sunday Israel would not be worn down by persistent rocket fire, warning it would hit any place from which militants were firing, including homes.

His remarks came as the air force stepped up its campaign against rocket fire, bombarding a 12-storey residential block.

But by early Monday, there was increasing talk about a possible new ceasefire agreement which would see the delegations return to Cairo to resume discussions on an Egyptian proposal to broker a more permanent end to the violence.

- Waiting for Israel -

"There is an idea for a temporary ceasefire that opens the crossings, allows aid and reconstruction material, and the disputed points will be discussed in a month," a senior Palestinian official told AFP in Cairo.

"We would be willing to accept this, but are waiting for the Israeli response to this proposal," he said, requesting anonymity because of the sensitivity of the negotiations.

Another Palestinian official said Egypt might invite Palestinian and Israeli negotiating teams to return to Cairo within 48 hours.

"Efforts are ongoing to reach an agreement," Hamas spokesman Sami Abu Zuhri told AFP, without going into specifics.

Daud Shihab, Islamic Jihad's spokesman, confirmed such efforts were under way.

"The success of contacts (talks) to reach a ceasefire depends on Palestinian demands being met," he said.

There was no immediate comment from Israel, with Netanyahu's spokesman Mark Regev saying Israel's position of no negotiations under fire had "not changed".

But Israeli Science Minister Yaakov Peri, an observer at the security cabinet and former head of the Shin Bet internal security agency, said if the rocket fire stopped, it was likely talks would resume.

"If a ceasefire goes into effect, and it sticks, there is a good chance that the prime minister will instruct the delegation to return to the talks in Cairo," he told public radio, saying it would be over a "lean arrangement."

"Generally, we will agree to open the crossings," he said, referring to Erez and the Kerem Shalom commercial crossing where humanitarian aid passes, which Israel was "also willing to increase".

Regarding the Rafah crossing with Egypt, "that is a decision for the Egyptians," although Israel would support the deployment of Palestinian Authority security personnel at the terminal, he said, defining the broad outline of a lean arrangement.

But a more comprehensive arrangement -- involving Israel facilitating the reconstruction of Gaza in exchange for its demilitarisation -- was "far off", he said.

- West Bank teen dies -

The invitation to new truce talks came after Egyptian leader Abdel Fattah al-Sisi met Palestinian president Mahmud Abbas on Saturday.

Egypt has repeatedly urged all parties to accept an open-ended truce and return to the negotiating table in Cairo.

Previous temporary ceasefires have failed to result in any agreement, although back-to-back extensions have given millions of people periods of relief from incessant bombardment and rocket fire.

Hamas, the de facto authority in Gaza, says any truce must provide for a lifting of Israel's crippling eight-year blockade and the opening of a seaport and airport, while Israel has demanded Gaza be demilitarised.

Meanwhile, senior Palestine Liberation Organisation official Wasel Abu Yusef told AFP the Palestinian leadership is to demand the UN Security Council set a deadline for ending the Israeli occupation.

Such a move would likely be vetoed by the United States which traditionally opposes any step perceived as anti-Israeli at the Security Council.

In the northern West Bank, a 14-year-old Palestinian died of wounds sustained Friday in clashes during a protest against the Gaza war. At least 20 Palestinians have been killed during such protests since July 8, UN figures show.

Elsewhere, Iran said it would "accelerate" moves to arm West Bank Palestinians a day after claiming it had shot down an Israeli drone above one of its uranium enrichment sites.