US Vice President JD Vance has arrived in Israel, as Washington tries to stabilise the first, shaky, phase of the Gaza ceasefire and push Israel and Hamas towards the harder concessions asked of each side in coming talks.
The two sides have accused each other of repeated breaches of the ceasefire since it was formally agreed eight days ago, with flashes of violence and recriminations over the pace of returning hostage bodies, bringing in aid and opening borders.
However, US President Donald Trump's 20-point ceasefire plan will require much more difficult steps to which the sides have yet to fully commit, including the disarmament of Hamas and steps towards a Palestinian state.
Mr Trump earlier warned Hamas it would be "eradicated" if it breaches the deal, but said he would give the Palestinian militant group a chance to honour the truce.
"We made a deal with Hamas that they're going to be very good, they're going to behave, they're going to be nice," Mr Trump told reporters at the White House as he hosted Australian Prime Minister Anthony Albanese.
"And if they're not, we're going to go and we're going to eradicate them, if we have to. They'll be eradicated, and they know that," he added.
US President Trump says Hamas will be handled 'toughly but properly'
Mr Trump helped broker the Gaza deal nearly two weeks ago but it has repeatedly come under threat as Israel accuses Hamas of stalling on handing over dead hostages, and of launching attacks.
"They got very rambunctious, and they did things that they shouldn't be doing, and if they keep doing it, then we're going to go in and straighten it out, and it'll happen very quickly," he said.

Mr Trump said that Hamas was now far weaker, especially as regional backer Iran was now unlikely to step in on its behalf following US and Israeli strikes this year.
"They don't have the backing of really anybody anymore. They have to be good, and if they're not good, they'll be eradicated," President Trump stressed.
Mr Trump's special envoy Steve Witkoff and adviser son-in-law Jared Kushner met Israeli Prime Minister Benjamin Netanyahu yesterday to discuss "developments and updates in the region", a spokesman for the prime minister's office said.

It comes as Israel said it has received the remains of another Gaza hostage handed over as part of the US-brokered ceasefire deal.
"Israel has received, through the Red Cross, the coffin of a missing hostage who was handed over to the IDF (military) and Shin Bet forces inside the Gaza Strip," a statement from the prime minister's office said.
The military and Shin Bet later confirmed the remains were back in Israel, and were being sent to "the National Institute for Forensic Medicine, where identification procedures will be carried out".
A senior Hamas official said the group's armed wing had handed over the captive's remains to the Red Cross after receiving them from the Abu Ali Mustafa Brigades - the armed wing of the Marxist-Leninist movement the Popular Front for the Liberation of Palestine (PFLP).