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President Donald Trump said Monday that the remaining Israeli hostages will only be returned once Hamas is "confronted and destroyed," as the Gaza-based terrorist group cited alleged progress in ongoing ceasefire talks. 

The U.S. and Israel pulled their negotiators from Qatar last month, with Trump's special envoy Steve Witkoff saying at the time that Hamas demonstrated a "lack of desire to reach a ceasefire in Gaza" and were likely not negotiating in good faith. 

"We will only see the return of the remaining hostages when Hamas is confronted and destroyed!!!" Trump wrote on TRUTH Social on Monday morning. 

"The sooner this takes place, the better the chances of success will be," Trump wrote. "Remember, I was the one who negotiated and got hundreds of hostages freed and released into Israel (and America!). I was the one who ended 6 wars, in just 6 months. I was the one who OBLITERATED Iran’s Nuclear facilities. Play to WIN, or don’t play at all! Thank you for your attention to this matter!" 

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The message came ahead of Trump's meeting with Ukrainian President Volodymyr Zelenskyy and European leaders at the White House on Monday as they try to iron out a separate peace deal with Russia. 

Meanwhile, in the Middle East, the Iran-backed Hamas said Monday it has accepted a new proposal from Arab mediators for a ceasefire in the Gaza Strip that would still need Israel’s approval. 

Israeli Prime Minister Benjamin Netanyahu said in response that Hamas is under "enormous pressure" after Israel announced plans to reoccupy Gaza City and other heavily populated areas after ceasefire negotiations again stalled in Qatar last month.

"I hear the media reports – and from them, you can draw one conclusion: Hamas is under enormous pressure," Netanyahu said in a Hebrew video statement translated by Fox News. 

Netanyahu also said on Monday he visited the Gaza Division, where he met with the senior Israeli Defense Forces command staff, and expressed "tremendous appreciation for the great achievements of the IDF in the War of Rebirth – the war on seven fronts." The prime minister said he was "deeply impressed by the fighting spirit and determination to complete the defeat of Hamas and to bring about the release of all our hostages." 

He said he also spoke to the defense minister and chief of staff "about our plans regarding Gaza City and the completion of our missions."

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A diplomat briefed on the negotiations with Hamas told Fox News that "through pressure on Hamas to accept, Qatari and Egyptian mediators secured a breakthrough that preserves 98% of the Witkoff proposal, which the Israeli side had previously agreed to." 

"The mediators were able to secure this outcome despite recent events and developments moving toward further escalation," the diplomat said. "This step marks the beginning of the road to a comprehensive solution."

Egyptian Foreign Minister Badr Abdelatty said mediators are "exerting extensive efforts" to revive a U.S. proposal for a 60-day ceasefire, during which some hostages would be released and the sides would negotiate a lasting ceasefire and the return of the rest. He spoke during a visit to Egypt’s Rafah crossing with Gaza, which has not functioned since Israel seized the Palestinian side in May 2024. He was accompanied by Mohammad Mustafa, the prime minister of the Palestinian Authority. 

Abdelatty said Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani had joined the talks, which include senior Hamas leader Khalil al-Hayya, who arrived in Cairo last week. He said they are open to other ideas, including a comprehensive deal that would release all the hostages at once.

Bassem Naim, a senior Hamas official, later told the Associated Press that the terrorist group had accepted the proposal introduced by the mediators, without elaborating.

An Egyptian official, speaking to the AP on condition of anonymity to discuss the sensitive talks, said the proposal includes changes to Israel’s pullback of its forces and guarantees for negotiations on a lasting ceasefire during the initial truce. The official said it is almost identical to an earlier proposal accepted by Israel, which has not yet joined the latest talks.

Netanyahu has vowed to continue the war until all the hostages are returned and Hamas has been disarmed, and to maintain lasting security control over Gaza. 

Hamas has said it will only release the remaining hostages in exchange for a lasting ceasefire and an Israeli withdrawal.

Fox News' Yonat Friling and the Associated Press contributed to this report.