The truce that went into effect on January 19 largely halted more than 15 months of Israeli war on the Gaza Strip and saw five groups of Israeli captives freed in exchange for hundreds of Palestinians in Israeli custody.
But tensions have been running high since a shock proposal by Trump to take over the Gaza Strip and remove its more than two million inhabitants.
Trump said Monday he would call for the end of the ceasefire if every Israeli captive was not released by noon on Saturday.
"But as far as I'm concerned, if all of the hostages aren't returned by Saturday 12 o'clock -- I think it's an appropriate time -- I would say cancel it and all bets are off and let hell break out," Trump told reporters at the White House.
The ceasefire agreement says staggered releases should take place over the ongoing 42-day first phase of the deal.
A spokesman for Hamas's armed wing, the Ezzedine al-Qassam Brigades, said in a statement earlier Monday that the next captive release, "which was scheduled for next Saturday, February 15, 2025, will be postponed until further notice".
The spokesman, Abu Ubaida, said the resumption of captive-prisoner exchanges was "pending the (Israeli) occupation's compliance and retroactive fulfilment of the past weeks' obligations".
The group accuses Israel of failing to carry out its commitments under the truce in time and of violating the ceasefire, including on humanitarian aid deliveries and after the Sunday deaths of three Gazans.
In a later statement, Hamas said it had "intentionally" made the announcement five days before the next exchange to allow mediators ample time to pressure Israel "towards fulfilling its obligations. The door remains open for the prisoner exchange batch to proceed as planned, once the occupation complies."
Israel said its military was readying for "any possible scenario".
'Complete violation'
Negotiators were due to meet in the coming days in Qatar to discuss the implementation of the truce's first phase, as well as potentially the next phases which have yet to be finalised.
Talks on a second phase were meant to begin on the truce's 16th day, but Israel had refused to send its negotiators to Doha for that.
The "Hostage and Missing Families Forum" campaign group said on Monday it had "requested assistance from the mediating countries to help restore and implement the existing deal effectively".
Israeli Defence Minister Israel Katz said the Hamas announcement was a "complete violation" of the ceasefire agreement, signalling that fighting could resume.
"I have instructed the IDF (military) to prepare at the highest level of alert for any possible scenario in Gaza," Katz said in a statement.
The military later said that it had raised "the level of readiness" around Gaza, and "decided to significantly reinforce the area".
Trump on Jordan, Egypt
On Sunday, Israeli Prime Minister Benjamin Netanyahu praised Trump's proposal to displace Gazans as "revolutionary", striking a triumphant tone in a statement to his cabinet following his return from Washington.
The proposal, which the United Nations and experts have said would violate international law, has already drawn widespread criticism.
Trump said Monday he could "conceivably" halt aid to US allies Jordan and Egypt if they refuse to take in Palestinians under his controversial Gaza plan.
Trump is due to meet Jordan's King Abdullah II in Washington this week.
The threat to withhold aid came after Cairo's foreign ministry said it rejected "any compromise" of Palestinian rights, including "remaining on the land".
Trump told Fox News Channel's Bret Baier earlier Monday that Palestinians would not have the right to return to Gaza.
"I'm talking about building a permanent place for them because if they have to return now, it'll be years before you could ever -- it's not habitable," said Trump of the devastated Gaza Strip.
Asked if the Palestinians would have the right to return, Trump said: "No, they wouldn't, because they're going to have much better housing."
For Palestinians, any attempt to force them out of Gaza would evoke dark memories of what the Arab world calls the "Nakba" or catastrophe -- the mass displacement of Palestinians during Israel's creation in 1948.
Despite Trump's words, displaced Gazans continued to stream back to their homes after Israeli forces withdrew from the Netzarim Corridor that cut the territory in two.
US and Egyptian security personnel were on the ground inspecting vehicles crossing the corridor, with one Gazan telling AFP the staff were "respectful" but the searches were "slow and trying".
Ahmed al-Rai said "It takes 20 minutes to inspect each vehicle" and that he had to wait five hours for his turn.
'Ill-treatment'
The Israeli war on Gaza was triggered on October 7, 2023, when Hamas took 251 captives, of whom 73 remain in Gaza, including 34 the Israeli military says are dead.
The health ministry in Gaza says the war has killed at least 48,208 people in the territory, mostly women and children.
Under the current ceasefire, Israel and Hamas on Saturday completed their fifth captive-prisoner exchange, with three Israeli captives and 183 Palestinian prisoners released.
UN Human Rights Office spokesman Thameen Al-Kheetan said that the "images of emaciated Israeli hostages and Palestinian detainees released" were "deeply distressing".
The Israelis freed "show signs of ill-treatment and severe malnourishment, reflecting very dire conditions they were subjected to in Gaza", he said.
"Israel and Hamas must ensure humane treatment, including freedom from any form of torture or abuse, for all those held under their power."
Netanyahu's office said "all the families of the hostages were informed" of Hamas's announcement on Monday and "made aware that the State of Israel is committed to respecting the agreement".
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