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 stated 200 fighters were trapped, although this number has not been confirmed. According to media reports, Kushner and Israeli Prime Minister Benjamin Netanyahu discussed the issue during a meeting in Jerusalem.

Hamas has previously stated that the trapped fighters will not surrender and has demanded safe passage, which Israel has rejected.

An Israeli government spokeswoman reported that Netanyahu and Kushner discussed phase one of the negotiations, which focuses on bringing the remaining hostages home, and the future of phase two, which includes disarming Hamas and demilitarizing Gaza.

The war in Gaza, which erupted following the Hamas-led attack on Israel on October 7, 2023, has caused extensive casualties, with over 69,000 reported killed in Gaza to date.

The first phase of the ceasefire focused on halting hostilities, securing the return of hostages, and facilitating humanitarian aid to Gaza. However, ongoing mutual accusations of violations by both sides raise concerns regarding the integrity of the ceasefire.

As the negotiations stall, there is an increasing fear of a de-facto partition of Gaza, as well as regional apprehensions about the implications of such a division.