Mr Netanyahu, who is hosting Antony Blinken, the US secretary of state, in Tel Aviv on Tuesday morning, is scheduled to meet this evening with Itamar Ben-Gvir, his national security minister, who is staunchly opposed to a ceasefire.
On Monday, top Western officials including Mr Blinken and David Cameron urged Hamas to accept an “extraordinarily generous” deal on the table.
A Hamas delegation has already left Cairo where the mediated talks are being held and are expected to return on Wednesday with a written response to the proposal.
Senior US officials previously complained that Yahya Sinwar, Hamas’ leader in Gaza, appeared to be the only stumbling block to the deal.
Israel has reportedly moderated its demand of getting 40 vulnerable hostages released in the first phase of the deal to 33, whereas Hamas insists it does not have more than 20 hostages who would be female, underage, injured or elderly.