The first round of Gaza talks between Hamas and mediators have ended in Egypt "amid a positive atmosphere", Egyptian state-linked media reported early on Tuesday.
Al-Qahera News, which is linked to state intelligence, reported the talks will continue on Tuesday, also between Hamas and mediators in the resort town of Sharm El-Sheikh, where an Israeli delegation arrived on Monday.
Behind closed doors and under tight security, negotiators were to speak through mediators shuttling back and forth, only weeks after Israel tried to kill Hamas's lead negotiators in a strike on Qatar.
Al-Qahera News earlier said delegations were "discussing preparing ground conditions for the release of detainees and prisoners".
"Egyptian and Qatari mediators are working with both sides to establish a mechanism" for the release of hostages held in Gaza in exchange for Palestinians held in Israeli jails, it said.
Trump told reporters at the White House he was "pretty sure" a peace deal was possible.
"I think Hamas has been agreeing to things that are very important... I think we're going to have a deal."
Hamas's lead negotiator Khalil al-Hayya, who survived Israel's attack on the Palestinian movement's leaders in Doha last month, held a meeting with Egyptian intelligence officials ahead of the talks, an Egyptian security source told news agency AFP.
This round of negotiations, launched on the eve of the second anniversary of Hamas's October 7, 2023 attack followed by the war, "may last for several days", Palestinian source close to Hamas's leadership told AFP.
"We expect the negotiations to be difficult and complex, given the occupation's intentions to continue its war of extermination," he told AFP.
Trump, whose envoy Steve Witkoff and son-in-law Jared Kushner are expected in Egypt, has urged negotiators to "move fast" to end the war in Gaza, where Israeli strikes continued on Monday.
Israel and Hamas are expected to engage in indirect talks on the details of a proposal by Trump for a hostage-prisoner exchange and long-term ceasefire.
Both Hamas and Israel have responded positively to Trump's proposal, but reaching an agreement on the details is set to be a huge task.
The plan envisages the disarmament of Hamas, which the group is unlikely to accept.
It also provides for the gradual withdrawal of Israeli forces from Gaza, but Israel's Prime Minister Benjamin Netanyahu has vowed to redeploy troops "deep inside" the territory while securing the release of hostages.
According to AFP, citing its Palestinian source, the initial hostage-prisoner exchange will "require several days, depending on field conditions related to Israeli withdrawals, the cessation of bombardment and the suspension of all types of air operations".
Negotiations will look to "determine the date of a temporary truce", a Hamas official said, as well as create conditions for a first phase of the plan, in which 47 hostages held in Gaza are to be released in return for hundreds of Palestinian detainees.
The International Committee of the Red Cross said it was ready to help with hostage and detainee returns and to facilitate aid access across Gaza, where the UN has declared a famine.
Military halt
AFP reported that its Palestinian source close to Hamas said it would halt its military operations in parallel with Israel stopping its bombardment and withdrawing its troops from Gaza City.
Israeli military chief Lieutenant General Eyal Zamir however warned that if the negotiations failed, then the military would "return to fighting" in Gaza.
Militants seized 251 hostages during their October 7, 2023 attack, 47 of whom are still in Gaza. Of those, the Israeli military says 25 are dead.
According to Trump's plan, in return for the hostages, Israel is expected to release 250 Palestinian prisoners with life sentences and more than 1,700 detainees from Gaza taken during the war.
Hamas has insisted it should have a say in the territory's future, though Trump's roadmap stipulates that it and other factions "not have any role in the governance of Gaza".
Under the proposal, administration of the territory would be taken up by a technocratic body overseen by a transitional authority headed by Trump himself.
Hamas's October 2023 attack resulted in the deaths of 1,219 people, mostly civilians, according to Israeli figures.
Israel's genocidal response has killed at least 67,160 Palestinians, according to health ministry figures in the territory that the United Nations considers reliable.