US President Donald Trump’s envoy and son-in-law, Jared Kushner, returned to Israel on Monday, as mediators face a new obstacle in their efforts to advance negotiations on the fragile Gaza ceasefire deal to the next and more complex phase.

Key sticking points remain unresolved, including Hamas’s disarmament, the reconstruction and future governance of Gaza, and the deployment of an international security force to the territory.

Without a timeline for the discussions, which are likely to require significant concessions from both Israel and Hamas, there are doubts that any progress can be achieved.

Another challenge has emerged recently, involving scores of Hamas fighters believed to be in tunnels beneath the southern city of Rafah behind the so-called “Yellow Line”, which marks the area under Israeli control.

Last week, US special envoy Steve Witkoff said an amnesty could be offered for fighters who laid down their arms, and that this could be a “model” for what Washington hoped to apply in the rest of Gaza.

Witkoff said 200 fighters were trapped, although this number has not been confirmed.

According to media reports, Kushner and the Israeli Prime Minister, Benjamin Netanyahu, discussed the issue during a meeting in Jerusalem on Monday.

Hamas has previously said the fighters will not surrender and demanded that they are given safe passage, which has so far been rejected by Israel.

An Israeli government spokeswoman said Netanyahu and Kushner had “discussed phase one, which we are currently still in, to bring our remaining hostages, and the future of phase two of this plan, which includes the disarming of Hamas, demilitarising Gaza, and ensuring Hamas will have no role in the future of Gaza ever again”.

The war in Gaza was triggered by the Hamas-led attack on southern Israel on 7 October 2023, when about 1,200 people were killed and 251 others were taken hostage.

Since then, more than 69,000 people have been killed by Israeli attacks in Gaza, according to the Hamas-run health ministry, whose figures the UN considers reliable.

The first phase of the ceasefire, which came into force last month, focused on halting the war, returning all hostages, and securing a surge in humanitarian aid into Gaza.

Twenty living hostages and the remains of 24 deceased captives have been released, with four bodies remaining in Gaza.

In return, Israel has freed 250 Palestinian prisoners from its jails and 1,718 detainees from Gaza who were being held without charge or trial. It has also handed over the remains of 315 Palestinians from Gaza.

Both Israel and Hamas have accused each other of violating the truce, with Israel saying Hamas has deliberately delayed the return of the remains of hostages and Hamas saying that Israel has killed at least 240 Palestinians and is restricting the entry of aid supplies.

Hamas has previously rejected disarmament, saying it would only do so once a Palestinian state has been established. Israel refuses any involvement in the governance of Gaza by the Western-backed Palestinian Authority, which is the body that governs parts of the occupied West Bank. Countries are reluctant to commit troops to the multinational force without clear goals, concerned that their soldiers might end up confronting fighters from Hamas and other Palestinian factions.

The Israeli military currently occupies 53% of Gaza’s territory and is expected to withdraw further in the next stage of the plan.

With no indication of imminent advances in the negotiations, a de-facto partition of Gaza between the area controlled by Israel and another ruled by Hamas was increasingly likely, sources told the Reuters news agency, with talks about reconstruction apparently likely to be limited to the Israel-controlled territory.

Arab countries have already expressed concerns that the current separation could become a permanent partition of Gaza.

The Trump plan does not include a pathway to Palestinian statehood – a concept which Israel rejects.

The Israeli military says it has identified a body handed over from Gaza as that of Israeli-Argentinian Lior Rudaeff.

The 61-year-old was killed while attempting to defend Nir Yitzhak kibbutz during the Hamas attack on southern Israel on 7 October 2023 and his body was taken to Gaza by the Palestinian Islamic Jihad (PIJ) armed group, the military said.

PIJ said the body was found on Friday in Khan Younis in southern Gaza.

Hamas has now returned all 20 living hostages and 23 out of 28 deceased hostages under the first phase of a ceasefire deal that started on 10 October. Four of the five dead hostages still in Gaza are Israelis and one is Thai.

Israel has criticised Hamas for not yet returning all the bodies. Hamas says it is hard to find them under rubble.

PIJ is an armed group allied with Hamas. It took part in the 7 October attack and previously held some Israeli hostages.

The Hostages and Missing Families Forum, a campaign group, welcomed the return.

“Lior’s return provides some measure of comfort to a family that has lived with agonising uncertainty and doubt for over two years,” it said in a statement. “We will not rest until the last hostage is brought home.”

During the first phase of the US-brokered ceasefire deal, Israel freed 250 Palestinian prisoners in its jails and 1,718 detainees from Gaza.

Israel has also handed over the bodies of 300 Palestinians in exchange for the bodies of the 20 Israeli hostages returned by Hamas, along with those of three foreign hostages – one of them Thai, one Nepalese and one Tanzanian.

The parties also agreed to an increase of aid to the Gaza Strip, a partial withdrawal of Israeli forces, and a halt to fighting, although violence has flared up as both sides accused one another of breaching the deal.

Israel launched air strikes after accusing Hamas fighters of killing two of its soldiers on 19 October and of killing another soldier on 28 October. Hamas said it was unaware of clashes in the area of the first incident and had no connection to the second attack.

Israeli military actions have killed at least 241 people since the start of the ceasefire, according to the Hamas-run health ministry, whose figures are seen by the UN as reliable.

The Israeli military launched a campaign in Gaza in response to the 7 October 2023 attack, in which Hamas-led gunmen killed about 1,200 people in southern Israel and took 251 others hostage. All but one of the dead hostages still in Gaza were abducted in the attack.

At least 69,169 people have been killed by Israeli attacks in Gaza since then, the health ministry reported.

From an embankment overlooking Gaza City, there’s no hiding what this war has done.

The Gaza of maps and memories is gone, replaced by a monochrome landscape of rubble stretching flat and still for 180 degrees, from Beit Hanoun on one side to Gaza City on the other.

Beyond the distant shapes of buildings still standing inside Gaza City, there’s almost nothing left to orient you here, or identify the neighbourhoods that once held tens of thousands of people.

This was one of the first areas Israeli ground troops entered in the early weeks of the war. Since then they have been back multiple times, as Hamas regrouped around its strongholds in the area.

Asked about the level of destruction in the area we visited, Israeli military spokesman Nadav Shoshani said it was “not a goal”.

“The goal is to combat terrorists. Almost every house had a tunnel shaft or was booby-trapped or had an RPG [rocket-propelled grenade] or sniper station,” he said.

“If you’re driving fast, within a minute you can be inside of a living room of an Israeli grandmother or child. That’s what happened on October 7.”

More than 1,100 people were killed in the Hamas attacks on Israel on 7 October 2023, and 251 others taken hostage.

Since then, more than 68,000 Gazans have been killed, according to the Hamas-run Health Ministry there.

The bodies of several hostages had been found in this area, Lt Col Shoshani said, including that of Itay Chen, returned to Israel by Hamas this week. Searches are continuing for the missing bodies of another seven hostages.

The Israeli military base we travelled to is a few hundred metres from the yellow line – the temporary boundary set out in US President Donald Trump’s peace plan, which divides the areas of Gaza still controlled by Israeli forces from the areas controlled by Hamas.

Israel’s army has been gradually marking out the yellow line with blocks on the ground, as a warning to both Hamas fighters and civilians.

There are no demarcations along this part of the line yet – a soldier points it out to me, taking bearings from a small patch of sand between the grey crumbs of demolished buildings.

The ceasefire is almost a month old, but Israeli forces say they are still fighting Hamas gunmen along the yellow line “almost every day”. The piles of bronze-coloured bullet casings mark the firing points on the embankments facing Gaza City.

Hamas has accused Israel of violating the ceasefire “hundreds of times”, and Gaza’s Hamas-run Health Ministry says more than 240 people have been killed as a result.

Col Shoshani said that Israeli forces were committed to the US-led peace plan, but that they would also make sure that Hamas no longer posed a threat to Israeli civilians, and would stay as long as necessary.

“It’s very clear to everyone that Hamas is armed and trying to control Gaza,” he said. “This is something that will be worked out, but we’re far from that.”

The next stage of the US-led plan requires Hamas to disarm and hand over power to a Palestinian committee overseen by international figures including President Trump.

But rather than give up its power and weapons, Col Shoshani said, Hamas was doing the opposite.

“Hamas is trying to arm itself, trying to assert dominance, assert control over Gaza,” he told me. “It’s killing people in broad daylight, to terrorise civilians and make sure they understand who is boss in Gaza. We hope this agreement is enough pressure to make sure Hamas disarms.”

Israeli forces showed us a map of the tunnels they said that soldiers had found beneath the rubble we saw – “a vast network of tunnels, almost like spider’s web” they said – some already destroyed, some still intact, and some they were still searching for.

What happens in the next stage of this peace deal is unclear.

The agreement has left Gaza in a tense limbo. Washington knows how fragile the situation is – the ceasefire has faltered twice already.

The US is pushing hard to move on from this volatile stand-off to a more durable peace. It has sent a draft resolution to UN Security Council members, seen by the BBC, which outlines a two-year mandate for an international stabilisation force to take over Gaza’s security and disarm Hamas.

But details of this next stage of the deal are thin: it’s not clear which countries would send troops to secure Gaza ahead of Hamas disarmament, when Israel’s troops will withdraw, or how the members of Gaza’s new technocratic administration will be appointed.

President Trump has outlined his vision of Gaza as a futuristic Middle Eastern hub, built with foreign investment. It’s a far cry from where Gaza is today.

Largely destroyed by Israel, and seen as an investment by Trump, the question is not just who can stop the fighting, but how much say Gazans will have in the future of their communities and lands.