Netanyahu discussed the plan with US Secretary of State Marco Rubio, who kicked off a Middle East visit by endorsing Israel's war aims in Gaza, saying Hamas "must be eradicated".
That created further doubt around the shaky ceasefire as talks on its second phase are yet to begin.
Rubio, in his upcoming stops in Saudi Arabia and the United Arab Emirates, is likely to face more pushback from Arab leaders over Trump's proposal, which includes redeveloping Gaza under US ownership.
Netanyahu has said all emigration from Gaza should be "voluntary", but rights groups and other critics say the plan amounts to coercion given the territory's vast destruction.
Netanyahu said he and Trump had a "common strategy" for Gaza.
Echoing Trump, he said "the gates of hell would be open" if Hamas did not release dozens of remaining hostages abducted in the militant group's attack on southern Israel on October 7, 2023, that triggered the 16-month war.
The ceasefire's first phase ends in two weeks.
Negotiations were meant to begin two weeks ago on the second phase, in which Hamas would release dozens of remaining hostages in exchange for more Palestinian prisoners, a lasting truce and the withdrawal of Israeli forces.
Trump's special Middle East envoy, Steve Witkoff, told Fox News that "phase two is absolutely going to begin" and he had "very productive" calls Sunday with Netanyahu and officials from Egypt and Qatar, which serve as mediators, about continuing talks this week.
He also said hostages to be released include 19 Israeli soldiers and "we believe all of them are alive".
Netanyahu's office said Israel's security cabinet would meet Monday to discuss the second phase.
Trump later told journalists it is "up to Israel what the next step is, in consultation with me".
In another sign of closing ranks, Israel's defence ministry said it received a shipment of 900-kilogram MK-84 munitions from the United States.
The Biden administration paused a shipment of such bombs in 2024 over concerns about civilian casualties in Gaza.
Netanyahu has signalled readiness to resume the fighting after the ceasefire's current phase, though it could be a death sentence for remaining hostages.
Rubio said peace became impossible as long as Hamas "stands as a force that can govern or as a force that can administer or as a force that can threaten by use of violence" adding, "It must be eradicated."
Hamas reasserted control over Gaza when the ceasefire began in January, despite suffering heavy losses.
Netanyahu has offered Hamas a chance to surrender and send top leaders into exile.
Hamas has rejected that scenario and insists on Palestinian rule.
Spokesman Abdul Latif al-Qanou told The Associated Press the group accepted a Palestinian unity government or a technocratic committee to run Gaza.
Netanyahu instructed negotiators to leave for Cairo on Monday to discuss further implementation of the ceasefire's first phase, as issues over delivery of shelter materials continue.
The Israeli military, meanwhile, said it carried out an air strike on people who approached forces in southern Gaza.
The Hamas-run interior ministry said it killed three of its police officers while they secured the entry of aid trucks near Rafah on the Egyptian border.
In an interview last week, Rubio indicated that Trump's Gaza proposal was in part aimed at pressuring Arab states to make their own postwar plan that would be acceptable to Israel.
Rubio also appeared to suggest that Arab countries send troops to combat Hamas.
