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A renewed push is under way to end the bloodshed in Gaza as both Israel and Hamas speak to mediators about a long-stalled ceasefire plan.

Israeli Prime Minister Benjamin Netanyahu will convene a meeting of his security cabinet on Thursday to discuss the latest proposal from Hamas, an unnamed source in his office told Reuters news agency.

Hamas on Wednesday said it presented new “ideas” to Qatari, Egyptian and Turkish mediators on how to reach a ceasefire and captive-exchange deal. Israel confirmed it is “evaluating” Hamas’s “comments”, which it did not detail.

The development comes as Israel hammers southern Khan Younis – Gaza’s second-largest city – from where it ordered an estimated 250,000 Palestinians to flee, killing at least seven people in an air strike near its main hospital.

With Gaza’s death toll near 38,000 and conditions worsening daily for its inhabitants, both Israel and Hamas are under increased international pressure to reach a truce – most recently based on a United Nations-backed plan outlined by United States President Joe Biden in May.

However, competing interpretations of that deal, which break down the cessation of hostilities and exchange of captives into three stages, have brought negotiations to a standstill.

While the US insists Israel backs the deal, Prime Minister Netanyahu has repeatedly called it into question, promising not to end the war until Hamas is “eradicated”. Hamas, which has agreed to the framework of the deal, wants a commitment it will end the war for good.

Little headway in negotiations has occurred since June 11 when Hamas said it is ready to “deal positively” with the proposal, but made several “amendments” it described as minor.

In a sign talks are gaining new momentum, Hamas said it is again communicating with officials from Qatar, Egypt and Turkey with “the aim of reaching an agreement”.

“We exchanged some ideas with the mediator brothers with the aim of stopping the aggression against our Palestinian people,” a Hamas statement said.

Netanyahu’s office and the Mossad intelligence service confirmed the new approach almost straight away.

“The hostages deal mediators have conveyed to the negotiating team Hamas’s remarks on the outline … Israel is evaluating the remarks and will convey its reply to the mediators,” said an Israeli statement.

One source with knowledge of the talks, quoted by AFP news agency, said Qatari and American efforts to “bridge the remaining gaps” between Israel and Hamas have gone on in the background for weeks.

Rami Khouri, a fellow at the American University of Beirut, told Al Jazeera news of the revived talks is hopeful but key sticking points remain – including whether the agreement will end the war “completely” and how many Palestinian prisoners will go free in exchange for Israeli captives.

Political analyst Omar Baddar said there is “serious division” between Israel’s military and political establishment over how to proceed.

Military leaders, he told Al Jazeera, realise there is “no path to a better future for Israel out of this entire mess, and that it is time to simply end this war”. – Xinhua