According to the Israeli Channel 12, Gallant told families of captives held in Gaza that the captive-prisoner swap deal is "closer than ever."

Meanwhile, CNN quoted an Israeli source familiar with the negotiations as saying that both parties "appear to be on the brink of a framework agreement for a ceasefire and hostage release deal."

The source added that Israeli officials believe Hamas’ latest response will enable the two parties to engage in detailed negotiations to reach an agreement.

Moreover, Israel's cabinet was set to convene Thursday to discuss Hamas' latest response to a US-backed proposal for a phased ceasefire in Gaza.

Hamas confirmed Wednesday that it had sent its response to Egypt and Qatar, which are mediating the talks, without providing details.

A US official told AP the US administration was examining the response, calling it constructive but saying more work needed to be done.

According to Israeli Ynet News, US President Joe Biden is expected to speak with Israeli Prime Minister Benjamin Netanyahu on Thursday, following weeks of efforts to arrange a conversation between them.

This time, Biden agreed to the call to pressure Netanyahu into reaching a deal with Hamas, Ynet said.

Bridging the gap

Hamas political official Bassem Naim said that the group has neither accepted nor rejected the American proposal and has “responded with some ideas to bridge the gap” between the two sides, without elaborating.

Ismail Haniyeh, Hamas' top political leader, has "made contact with the mediator brothers in Qatar and Egypt about the ideas that the movement is discussing with them with the aim of reaching an agreement," the group said in a statement late Wednesday.

On Thursday, a Palestinian official close to the mediation effort told Reuters that Hamas has shown flexibility over some clauses that would allow a framework agreement for the release of captives to be reached should Israel approve.

US officials said the latest proposal has new language that was proposed to Egypt and Qatar on Saturday and addresses indirect negotiations that are set to commence during the first stage of the three-phase deal that Biden laid out in a 31 May speech.

The first phase calls for a “full and complete ceasefire,” a withdrawal of Israeli forces from all densely populated areas of Gaza and the release of a number of captives, including women, older people and the wounded, in exchange for the release of hundreds of Palestinian prisoners.

The proposal called for the parties to negotiate the terms of the second phase during the 42 days of phase one.

Under the current proposal, Hamas could release all of the remaining men, both civilians and soldiers, during the second phase. In return, Israel could free an agreed-upon number of Palestinian prisoners and detainees.

The releases wouldn't occur until “sustainable calm” takes effect and all Israeli troops withdraw from Gaza. The third phase would see the return of the remains of captives.

The transition from the first to the second phase has appeared to be the main sticking point.

Hamas is concerned that Israel will restart the war after the first phase, perhaps after making unrealistic demands in the talks.

In a lengthy television interview last month, Netanyahu said that he was prepared to make a “partial deal,” but was committed to continuing the war “after a pause” in order to annihilate Hamas. Later, speaking before Israel's parliament, he said Israel remains committed to the deal outlined by Biden.

As ceasefire talks appeared to be gaining new steam, the Palestinian Health Ministry said Thursday that the Palestinian death toll from nearly nine months of the Israeli war on Gaza has surged past 38,000.

The ministry said that in the last 24 hours, the bodies of 58 people killed in Israeli bombardment had been brought to hospitals, bringing the overall death toll to 38,011.

It said more than 87,000 people have been wounded in Gaza since the war began on 7 October.