The current hostage deal negotiations focus on the release of ten hostages held in the Gaza Strip in one phase, Prime Minister Benajamin Netanyahu told the family of hostage Eitan Mor, Israeli media reported on Monday.
Later on Monday, National Unity leader Benny Gantz called for the return of the hostages, noting "time is good only for Hamas and bad for the hostages. A plan to release all the hostages is what is best for Israel – security-wise, socially, and morally."
On Sunday night, Saudi state-owned Al-Arabiya news outlet reported that Hamas has agreed to the release of additional hostages in two stages, as well as to provide up-to-date information on the remaining hostages.
Mediators are currently in the final stages of drafting the ceasefire agreement, with the US striving to reach an agreement before the end of this month, the report noted.
The discussion on expelling Hamas's top leadership from Gaza has been postponed to a later date, according to the report.
On Sunday, a source in Hamas told the Saudi-owned "Asharq" channel that a negotiating delegation for the terror group, headed by Khalil al-Hayya, would meet in Cairo with senior Egyptian and Qatari officials, as part of efforts to reach a ceasefire agreement.
Talks have been held between Israel, Egypt, and the US in an attempt to bring the Egyptian proposal near to that of Israel.
Trump says US 'close to getting hostages back'
On Thursday, Israeli officials told The Jerusalem Post that there had been "some movement" with regard to the hostage deal negotiations, noting the chances of reaching a deal while US President Donald Trump said the US was "close to getting hostages in Gaza back."
Amichai Stein contributed to this report.