In a brief statement late Saturday, Netanyahu said he has sent a delegation to Egypt "to finalise technical details," adding that "our goal is to contain these negotiations to a time frame of a few days".
He spoke after Hamas said it had accepted some elements of the US plan.
President Donald Trump welcomed the Hamas statement but on Saturday warned that "Hamas must move quickly, or else all bets will be off".
Meanwhile, Israeli bombing of Gaza City has "significantly subsided".
Israel has moved to a defensive-only position in Gaza and will not actively strike, said an official who was not authorised to speak to the media on the record.
The official said no forces have been removed from the territory.
Still, Shifa Hospital director Mohamed Abu Selmiyah told the AP on Saturday that Israeli strikes killed five Palestinians across Gaza City, while bombing had "significantly subsided".
The army statement came hours after Trump ordered Israel to stop bombing Gaza once Hamas said it had accepted some elements of his plan.
Trump welcomed the Hamas statement, saying: "I believe they are ready for a lasting PEACE".
Trump appears determined to deliver on pledges to end the war and return all hostages ahead of the second anniversary on Tuesday of the attack that sparked it.
His proposal, unveiled earlier this week, has widespread international support.
On Friday, Netanyahu's office said Israel was committed to ending the war that began when Hamas attacked Israel on October 7, 2023.
Netanyahu is under increasing pressure to end the conflict.
The official told the AP that Netanyahu put out the rare late-night statement on the Sabbath, saying that Israel has started to prepare for Trump's plan due to pressure from the US
A senior Egyptian official said US envoy Steve Witkoff will travel to Egypt to head the US negotiating team in the talks to release the Israeli hostages in exchange for Palestinians in Israeli detention.
Delegations from Israel and Hamas will join the talks, which will also discuss maps showing the expected withdrawal of Israeli forces from certain areas in Gaza, said the official who spoke on condition of anonymity.
The official involved in the ceasefire negotiations also said Arab mediators are preparing for a comprehensive dialogue among Palestinians aimed at unifying their position toward Gaza's future.
Under the plan, Hamas would release the remaining 48 hostages — around 20 of them believed to be alive — within three days.
It would also give up power and disarm.
In return, Israel would halt its offensive and withdraw from much of Gaza, release hundreds of Palestinian prisoners and allow an influx of humanitarian aid and eventual reconstruction.
Palestinians in Gaza tried to piece together what the plan means in real terms.
"I hope Hamas ends the war, because we are truly tired," said Mohammad Shaat in Khan Younis, as anxious Palestinians roamed the shattered streets.
