Israeli fire killed 10 Palestinians across Gaza on Monday, while Egypt proposed a new ceasefire that would open key crossings into the blockaded territory.
Since an earlier truce collapsed on August 19, the death toll in Gaza has risen steadily with at least 113 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 110 rockets were shot down.
Since midnight on Sunday, Israeli fire killed at least 10 Palestinians, including a woman, a 78-year-old man and a boy aged three.
Also among the dead was Abdullah Mortaja, 27, a freelance journalist who previously worked for Hamas's Al-Aqsa TV.
Medical officials said he was hit by tank fire in the war-battered Shejaiya area of eastern Gaza City.
Two people wounded previously died of their injuries on Monday, raising the Gaza death toll since the July 8 start of the campaign to 2,134 with 10,915 wounded, according to the emergency services.
On Monday night, a 17-year-old boy was killed and about 25 people were wounded in a strike on a Gaza City mosque, they said.
The Gaza religious affairs ministry said Israeli fire during the day destroyed four more mosques, raising to 71 the number of mosques destroyed over the past seven weeks.
On the Israeli side, 68 people have been killed, the vast majority soldiers.
On Monday, militants fired 107 rockets at Israel, of which 14 were shot down, one in the greater Tel Aviv area, the army said.
But there was also increasing talk about a possible new ceasefire agreement which would see delegations return to Cairo to resume discussions on an Egyptian proposal to broker a longer-term 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.
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"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, although probably not immediately.
"I don't think it will be a matter of a few hours," he told army radio. "I think this time Israel will try to make sure over several more hours or a day that the ceasefire is holding."
In a separate interview, he said: "Generally, we will agree to open the crossings," referring to Erez and the Kerem Shalom commercial crossing for humanitarian aid.
Regarding Gaza's 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 shape of an initial arrangement.
But a more comprehensive deal -- with 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 President Abdel Fattah al-Sisi met Palestinian leader Mahmud Abbas on Saturday.
Egypt has repeatedly urged all parties to accept an open-ended truce and return to the negotiating table in Cairo.
Abbas is expected to convene a meeting of the Palestinian leadership in the West Bank city of Ramallah on Thursday, a Palestinian official said without elaborating.
Previous temporary ceasefires have failed to produce 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.
In the northern West Bank, a 14-year-old Palestinian died of wounds sustained Friday in clashes with Israeli forces during a protest against the Gaza war.
At least 20 Palestinians have been killed during such protests since the conflict broke out, UN figures show.