Six months into its offensive against the Palestinian Islamist movement Hamas, Israel also voiced cautious optimism about the latest round of mediated negotiations.
Israel and Hamas sent teams to Egypt on Sunday, following the arrival on Saturday of CIA Director William Burns, whose participation followed US pressure for a deal that would free hostages held in Gaza and ease the humanitarian crisis there.
There was no immediate comment from Hamas on Monday.
In Jerusalem, Israeli Foreign Minister Israel Katz described the Cairo talks as the closest the sides have come to a deal since a November truce under which Hamas freed dozens of hostages.,
"We have reached a critical point in the negotiations," he told Israel's Army Radio.
"If it works out, then a large number of hostages will come home."
Hamas seized 253 people during an October 7 killing spree in southern Israel that triggered the war.
Of those, 129 hostages remain, and negotiators have spoken of about 40 going free in the first stage of a prospective deal with Hamas.
According to Al-Qahera, the Hamas and Qatar delegations left Cairo and will return within two days to agree on the terms of a final agreement, while the Israel and US delegations will leave within a few hours.
It said consultations would continue in the next 48 hours.
Hamas wants to parlay any deal into an end to the war, full withdrawal of all Israeli forces and return of displaced Gazans.
Israel has ruled out the first two demands, saying it would eventually topple Hamas.
Israeli Prime Minister Benjamin Netanyahu said on Sunday that despite growing international pressure, Israel would not give in to "extreme" Hamas demands.
But Israeli officials have signalled a willingness to allow some Palestinians displaced from northern Gaza to return there.
While saying he was more optimistic than before about a diplomatic breakthrough, Katz said: "Israel is poised to continue the war."
Thousands of Israeli protesters in Jerusalem rallied on Sunday demanding the government do more to recover the hostages.
Western countries have voiced outrage over what they see as an unacceptably high Palestinian civilian death toll and humanitarian crisis in Gaza that have resulted from Israel's campaign to destroy Hamas.
Hamas killed 1200 people in southern Israel on October 7, according to Israeli tallies.
More than 33,100 Palestinians have been killed in the Israeli response, according to the health ministry in Gaza.
Hamas has said it has lost 6000 fighters, while Israel says the number is twice as high.
More than 600 Israeli soldiers have been killed in Gaza combat, the army says.
