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 discussed phase one, focusing on returning hostages, while also addressing phase two, which includes disarming Hamas and ensuring it has no governance role in Gaza in the future.

The war in Gaza was triggered by the Hamas-led attack on southern Israel on October 7, 2023, which resulted in the deaths of approximately 1,200 people and the taking of 251 hostages. Since that date, over 69,000 people have reportedly died from subsequent Israeli attacks, according to the Hamas-run health ministry.

The current ceasefire, which aims to halt hostilities and ensure humanitarian aid delivery, has seen the release of living hostages and the transfer of prisoners. However, both sides have accused each other of violating the truce, complicating ongoing negotiations.

Hamas has categorically rejected disarmament, asserting it will only comply once a Palestinian state has been established. Meanwhile, Israel maintains a military presence over a significant portion of Gaza, leading to fears of a permanent partition of the territory.