Efforts to pause the fighting gained new momentum over the past week after Israel announced plans for a new offensive to seize control of Gaza City at the heart of the enclave.
Mediators Egypt and Qatar have been pushing to restart indirect talks between the sides on a US-backed ceasefire plan.
The proposal includes the release of 200 Palestinian convicts jailed in Israel and an unspecified number of imprisoned women and minors, in return for 10 living and 18 deceased hostages from the Gaza Strip, according to a Hamas official.
Two Egyptian security sources confirmed the details and added that Hamas has requested the release of hundreds of Gaza Strip detainees as well.
Israel says a total of 50 hostages remain in the enclave, 20 of them still alive.
"Israel's policy is consistent and has not changed. Israel demands the release of all 50 hostages in accordance with the principles established by the cabinet for ending the war. We are in the final decisive stage of Hamas and will not leave any hostage behind," an Israeli political source said.
The comment, while adamant, fell short of an outright rejection of the proposal on the table.
Prime Minister Benjamin Netanyahu was expected to convene discussions about the ceasefire proposal soon, the two Israeli officials said.
A response was expected in the coming two days, a Palestinian source close to the talks said.
Qatari foreign ministry spokesman Majed al-Ansari said the 60-day truce deal would include "a pathway to a comprehensive agreement to end the war".
The proposal includes a partial withdrawal of Israeli forces, which presently control 75 per cent of the Gaza Strip and the entry of more humanitarian aid into the enclave, where a population of 2.2 million people is increasingly facing famine.
Israel had previously agreed to the outline, advanced by US special Middle East envoy Steve Witkoff, but negotiations faltered over some of its details.
The last round of talks ended in deadlock in late July.
At a shelter in Khan Younis, in the south of the enclave, displaced people had mixed feelings over whether a deal would be reached this time.
"I expect - every time the (Israeli) occupation would be obstinate, reject and receive proposals with negative responses - I expect the same for this proposal as well," Abdallah al-Khawaja said.
Women sat by wood fires cooking meals for their families while men filled plastic gallons with water; many hoped Israel would approve the proposal.
"What I say and expect as a member of the Palestinian people living in the Gaza Strip, one of the bereaved and displaced, is that I expect a positive response (from Israel)," said Awad Labde.
Israel's plans to seize control of Gaza City have stirred alarm abroad and among the estimated one million people living there.
On the ground, there were no signs of a ceasefire nearing as Israeli gunfire, tank shelling and air strikes killed at least 20 Palestinians on Tuesday, according to Gazan health officials.
Tanks completed taking control of the Zeitoun suburb, an eastern neighbourhood on Gaza City's outskirts, and continued to pound the nearby area of Sabra, killing two women and a man, medics said.
Local health authorities said dozens of people had been trapped in their houses because of the shelling.
The Israeli military said it was checking the report.
Hamas official Izzat El-Reshiq said that the truce proposal it has agreed to is an interim accord that would pave the way for negotiations on ending the war.
A source close to the talks said that, unlike previous rounds, Hamas accepted the proposal with no further demands.
But prospects for agreeing an end to the war appear remote, with gaps remaining on the terms.
Israel is demanding the group lay down its arms and its leaders leave the enclave, conditions which Hamas has so far publicly rejected.
