Two officials who were at a security cabinet meeting on Thursday to approve the plan told Reuters that the evacuation of civilians from affected areas may only be completed by the start of October, giving time for a deal to be pursued.
The plan raised international alarm over the harm it could bring to the shattered enclave, where a hunger crisis has worsened.
On Sunday, Netanyahu summoned foreign journalists to explain the blueprint, which includes what he described as a surge of humanitarian aid.
Netanyahu said that Israel will first allow civilians to leave the battle zones before forces move in on Gaza City, which he described as one of Hamas' last two remaining strongholds, whose defeat will bring an end to the war.
But Israel's Finance Minister Bezalel Smotrich, a security cabinet member who has demanded even tougher action, said the plan was designed to pressure Hamas back to the negotiating table, rather than defeat the group and urged Netanyahu to scrap it.
Indirect negotiations between Israel and Hamas over a US proposal for a 60-day ceasefire that would have included the release of half the hostages still in Gaza ended last month in a deadlock, with major gaps still between both sides.
The mediators, Egypt and Qatar, have not given up on reviving negotiations, according to an Arab diplomat who said Israel's decision to broadcast its new Gaza City offensive plan may not be a bluff, but it also serves to bring Hamas back to the negotiating table.
The diplomat said that there was a new willingness from Hamas to engage in constructive talks toward a ceasefire after they had seen Netanyahu's seriousness about taking all of Gaza.
Senior Hamas official Basem Naim said the group had informed the mediators that it was still interested in reaching a ceasefire deal.
Netanyahu has not ruled out eventually opting for a deal.
A source close to the prime minister said that if a relevant proposal were to emerge, it would be brought before Israel's security cabinet.
Asked on Sunday whether he would halt the new offensive in favour of a ceasefire, Netanyahu publicly took a tougher stance.
"We are going to destroy Hamas, we are not stopping, we are advancing," he said.
He also said he had instructed the Israeli military to speed up its plans for the new offensive.
"I want to end the war as quickly as possible and that is why I have instructed the (Israel Defence Forces) to shorten the schedule for seizing control of Gaza City," he said.
The timeline, he said, was "fairly quickly".
But the plans laid out at the security cabinet on Thursday could take around five months to complete, according to the two officials present at the meeting.
But even with Hamas' top leaders dead and fighters long reduced to a guerrilla force scattered among the ruins of Gaza, Netanyahu faces scepticism over the new plan - including from his military chief, who called it a death trap - and of any hopes that it will end the war soon.
"This move is a danger to Israel and its security and it is pointless," said Israel's opposition leader Yair Lapid.
"The hostages will die, soldiers will die, the economy will fall apart and Israel's international standing will crumble."
