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The Israeli government has offered a new proposal to Hamas that would see a two-month ceasefire in return for the release of Israeli hostages, after rebuffing a Hamas offer.

The proposal was given to Egyptian and Qatari mediators following the approval by the Israeli war cabinet ten days prior, according to Israeli officials speaking toÌýAxios.

Israeli Prime Minister Benjamin Netanyahu earlier rejected of a Hamas' proposal for a prisoner swap that would see an end to Israel's war on Gaza.

"I reject outright the terms of the surrender of the monsters of Hamas," Netanyahu sad, arguing that such a deal would allow Hamas to remain "intact".Ìý

The new Israeli proposal would see a two-month ceasefire with Hamas in exchange for a staged release of the 136 remaining Israeli hostages.

The first stage would include the release of women and men over 60 and those in critical medical condition.

The second stage would include the release of female soldiers, men under 60 who are not soldiers, male soldiers, and the bodies of dead hostages.

Palestinian prisoners would also be released as part of the exchange, although according to Axios Israel will not agree to the release of all 6,000 prisoners, with negotiations over the number.

It is also unknown if any of the over 6,000 Palestinians that have been detained by the Israeli military since 7 October from the occupied West Bank will be included in the deal.

Israeli officials added that theÌýmilitary would withdraw from certain populated centres of Gaza as part of a redeployment, and allow Palestinians - forced out of their homes - back into northern Gaza.

The Israeli military has previously announced withdrawals from parts of northern Gaza, only to re-engage in battles in the city and conduct strikes which have killed many civilians.

Officials also added that further combat operations following the ceasefire would likely be smaller in scale and intensity, according to the officials.

Netanyahu informed the families of Israeli hostages in Gaza of the proposal during a meeting on Monday.

He told families that he believed the military's renewed action in Gaza was likely to pressure Hamas into agreeing, saying "I've passed [the proposal] on, and now there's a 'tug of war'".

Some 250 hostages were taken during Hamas' attack on Israel on 7 October, with 130 being released during a one-week ceasefire in November.Ìý

The Israeli initiative also comes following reports by CNN that Israel has proposed to Qatari officials that senior Hamas leaders could leave the strip as part of a broader ceasefire agreement.

The proposals were made by Mossad Chief David Barnea during two trips. During a visit to Warsaw in December, Barnea made the proposal to Qatari Prime Minister Mohammed bin Abdulrahman Al-Thani and CIA Director Bill Burns.

Barnea said in Doha this month that he made the proposals again to US Secretary of State Anthony Blinken, who reportedly said that the idea "would never work".

Families of the Israeli hostages have ramped up calls for their release, with protests occurring outside Netanyahu's house and inside the Israeli Knesset on Sunday.

UN agencies have repeatedly called for a ceasefire for an increase in humanitarian aid into Gaza, as UNRWA reports that 570,000 people face catastrophic hunger in the enclave.