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 air strikes on northern Gaza have killed four Palestinians, including two women and a three-year-old boy, medics said, raising the Palestinian death toll to 2,124 in seven weeks of violence.
On the Israeli side, 68 people have been killed, four of them civilians and the rest soldiers.
Another 38 rockets fired from Gaza struck the Israeli south on Sunday, while another was shot down, army statistics showed.
Following a weekend of heavy fire on the south, Prime Minister Benjamin Netanyahu insisted Israel would not be worn down by persistent rocket fire and that the operation would not end until quiet was restored.
"Our enemies... will not succeed in wearing us down. Against their attrition, they will be struck very hard," he said on Sunday, warning that Israel 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, firing missiles which levelled a 12-storey residential block.
But by early Monday, there was increasing chatter about a possible new ceasefire agreement which would see the delegations return to Cairo to resume talks 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 spokesperson Sami Abu Zuhri told AFP, without going into specifics.
And Daud Shihab, Islamic Jihad's spokesperson, also confirmed such efforts were under way.
"The success of contacts (talks) to reach a ceasefire depends on Palestinian demands being met," he told AFP.
There was no immediate comment from Israel, with Netanyahu's spokesperson Mark Regev refusing to comment on the matter and saying Israel's position of no negotiations under fire had "not changed".
Egypt has repeatedly urged all parties to accept an open-ended truce and return to the negotiating table in Cairo.
Israel withdrew its negotiators on August 19 after rocket fire on the south shattered a 24-hour truce some eight hours before it expired.
The Palestinian negotiating team left the Egyptian capital a day later, bringing the talks to a standstill.
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.
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.
"As soon as a ceasefire goes into effect, the two sides can sit down and discuss their demands," Abbas said.
Over the weekend, five rockets from the Syrian Golan Heights slammed into the Israeli-occupied side of the plateau early Sunday, just hours after a rocket fired from Lebanon hit the north, causing damage but no casualties.
And on Sunday a 14-year-old Palestinian from Nablus in the northern West Bank died of gunshot wounds sustained Friday in clashes with troops during a protest against the Gaza war.
At least 20 West Bank Palestinians have been killed during protests since the conflict began seven weeks ago, UN figures show.
Iran, meanwhile, said Monday it will "accelerate" arming Palestinians in the West Bank after saying on Sunday it had shot down an Israeli drone above the Natanz uranium enrichment site in the centre of the Islamic republic.