Indirect talks aimed at reaching a final agreement on a US peace plan to end the war in Gaza are set to continue on Tuesday in the Egyptian city of Sharm El-Sheikh.

Palestinian and Egyptian officials have told the BBC that the sessions are focused on "creating the field conditions" for a possible exchange that would see the release of all Israeli hostages in return for a number of Palestinian prisoners.

Israel's prime minister said on Saturday that he hoped to announce the release of hostages "in the coming days".

As the officials met on Monday, US President Donald Trump told reporters at the White House: "We have a really good chance of making a deal, and it'll be a lasting deal."

Hamas has said it agrees to the peace plan proposals in part, but has not responded to several key demands - including its disarmament and not having any future role in the governance of Gaza.

A senior Israeli security source said the talks initially would focus only on the release of hostages and give Hamas a few days to complete that phase.

The second day of the talks, which will see Egyptian and Qatari officials holding shuttle meetings with delegations from both Israel and Hamas separately, will be taking place on the second anniversary of the Hamas-led attack on southern Israel on 7 October 2023, in which about 1,200 people were killed and 251 others were taken hostage.

The Israeli military launched a campaign in Gaza in response. Since then, 67,160 have been killed by Israeli military operations in Gaza, including 18,000 children, according to the territory's Hamas-run health ministry.

UN Secretary-General Antonio Guterres said in a statement commemorating the 7 October anniversary that Trump's plan "presents an opportunity that must be seized to bring this tragic conflict to an end".

UK Prime Minister Sir Keir Starmer reiterated his support for the plan in his statement commemorating the anniversary, saying: "We welcome the US initiative towards peace in the Middle East, and this government will do everything in our power to bring about the day where every child of Israel can live peacefully, alongside their Palestinian neighbours, in safety and security."

These discussions are expected to be among the most consequential since the start of the war and could determine whether a path toward ending the conflict is finally within reach.

US special envoy Steve Witkoff, Trump's son-in-law Jared Kushner and Qatari foreign minister Sheikh Mohammed bin Abdulrahman Al Thani are among those attending.

Trump, writing on social media, has urged everyone involved in efforts to end the Gaza war to "move fast" and says he has been told the first phase of the peace plan - which includes the hostage release - "should be completed this week".

On Monday, he told reporters at the White House that "Hamas has been agreeing to things that are very important."

"I really think we're going to have a deal," he added.

A Palestinian official close to the negotiations told the Reuters news agency that the first session ended late Monday evening, and more talks were due to take place on Tuesday.

State-affiliated Al-Qahera News also said talks would continue on Tuesday – and that the first day had ended "amid a positive atmosphere".

The 20-point plan, which has been agreed upon by Trump and Israeli Prime Minister Benjamin Netanyahu, proposes an immediate end to fighting and the release of 48 hostages, only 20 of whom are thought to be alive, in exchange for hundreds of detained Gazans.

The plan stipulates that once both sides agree to the proposal "full aid will be immediately sent into the Gaza Strip".

It also states that Hamas would have no role in governing Gaza, and it leaves the door open for an eventual Palestinian state.

However, after the plan was announced publicly a week ago, Netanyahu reinstated his longstanding opposition to a Palestinian state, saying in a video statement: "It's not written in the agreement. We said we would strongly oppose a Palestinian state."

On Friday, Hamas responded to the proposal in a statement, in which the group agreed "to release all Israeli prisoners, both living and dead, according to the exchange formula contained in Trump's proposal" - if the proper conditions for the exchanges are met.

It did not specifically mention or accept Trump's 20-point plan but said it "renews its agreement to hand over the administration of the Gaza Strip to a Palestinian body of independents (technocrats), based on Palestinian national consensus and Arab and Islamic support."

The statement made no mention of the demands that Hamas agree to its disarmament and to playing no further role in the governance of Gaza.

It added that the part of the proposals dealing with the future of Gaza and the rights of Palestinian people was still being discussed "within a national framework", of which it said Hamas will be a part.

Many Palestinians described Hamas' response to the peace plan as unexpected, after days of indications that the group was preparing to reject or at least heavily condition its acceptance of Trump's peace plan proposal.

Instead, Hamas refrained from including its traditional "red lines" in the official statement, a move many interpret as a sign of external pressure.

European and Middle Eastern leaders have welcomed the proposal. The Palestinian Authority (PA), which governs parts of the Israeli-occupied West Bank, has called the US president's efforts "sincere and determined".

Iran - which has been one of Hamas's main sponsors for many years - has also now signalled its support for Trump's Gaza peace plan.

Israeli bombardment continued in several parts of the Gaza Strip on Monday ahead of the talks beginning.

Israel is carrying out an offensive in the city, which it has said is aimed at securing the release of the remaining hostages.

Mahmoud Basal, spokesman for Gaza's Hamas-run civil defence, told the BBC that "no aid trucks have been allowed into Gaza City since the offensive began four weeks ago".

"There are still bodies we cannot retrieve from areas under Israeli control," he said.

Hundreds of thousands of Gaza City residents have been forced to flee after the Israeli military ordered evacuations to a designated "humanitarian area" in the south, but hundreds of thousands more are believed to have remained.

Israel's defence minister has warned that those who stay during the offensive would be "terrorists and supporters of terror".

In the last 24 hours, 21 Palestinians have been killed in Gaza and a further 96 injured, the Hamas-run health ministry said in its latest update.

International journalists have been banned by Israel from entering the Gaza Strip independently since the start of the war, making verifying claims from both sides difficult. (BBC)