Ron Dermer, a top adviser to Prime Minister Benjamin Netanyahu, was set to travel to the US this week for talks on a ceasefire, an Israeli official said, and plans were being made for Netanyahu to travel there in the coming weeks, a sign there may be movement on a deal.
Netanyahu was meeting with his security cabinet on Sunday evening, the official said on condition of anonymity to discuss plans that had not been finalised.
"MAKE THE DEAL IN GAZA. GET THE HOSTAGES BACK!!!" Trump wrote on social media.
Trump raised expectations on Friday for a deal, saying there could be an agreement within the next week.
Trump has repeatedly called for Israel and Hamas to end the war.
An eight-week ceasefire was reached just as he took office earlier this year but Israel resumed the war in March after trying to get Hamas to accept new terms on next steps.
Some Palestinians greeted the possibility of a new truce with scepticism after watching the last ceasefire shattered.
"Since the beginning of the war, they have been promising us something like this: release the hostages and we will stop the war," said Abdel Hadi Al-Hour.
"They did not stop the war."
Trump also doubled down on his criticism of the legal proceedings against Netanyahu, who is on trial for alleged corruption, calling it "a POLITICAL WITCH HUNT".
In the post on Saturday evening, Trump said the trial interfered with ceasefire talks, saying Netanyahu "is right now in the process of negotiating a Deal with Hamas, which will include getting the Hostages back".
Talks between Israel and Hamas have repeatedly faltered over a major sticking point - whether the war should end as part of any ceasefire agreement.
Hamas official Mahmoud Merdawi accused Netanyahu of stalling progress on a deal, saying on social media that the Israeli leader insists on a temporary agreement that would free just 10 of the hostages.
About 50 hostages remain, with less than half believed to be alive.
Netanyahu spokesman Omer Dostri said that "Hamas was the only obstacle to ending the war," without addressing Merdawi's claim.
During a visit on Sunday to to Israel's internal security service Shin Bet, Netanyahu said that the Israel-Iran war and subsequent ceasefire have opened many opportunities: "First of all, to rescue the hostages. Of course, we will also have to solve the Gaza issue, to defeat Hamas, but I estimate that we will achieve both tasks."
Hamas says it is willing to free all the hostages in exchange for a full withdrawal of Israeli troops and an end to the war in the Gaza Strip.
Israel rejects that offer, saying it will agree to end the war if Hamas surrenders, disarms and goes into exile, something that the group refuses.
The war in the enclave began with the Hamas-led attack on southern Israel on October 7, 2023 in which militants killed 1200 people and took about 250 hostage.
Gaza's Health Ministry on Sunday said that another 88 people have been killed by Israeli fire over the past 24 hours, raising the war's toll among Palestinians to 56,500.
The ministry, which operates under the Hamas government, does not distinguish between militants and civilians in its count but says more than half of the dead are women and children.
The war has displaced most of the Gaza Strip's population, often multiple times, obliterated much of the territory's urban landscape and left people overwhelmingly reliant on outside aid, which Israel has limited since the end of the latest ceasefire.
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