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 stated that an amnesty could be offered for fighters who chose to lay down their arms, which might serve as a model for future negotiations throughout Gaza.

According to reports, Kushner and Israeli Prime Minister Benjamin Netanyahu discussed these critical issues during a meeting in Jerusalem. Hamas has made it clear that the fighters will not surrender and has requested safe passage, which Israel has so far rejected.

An Israeli government spokeswoman confirmed that discussions included the first phase of the ceasefire, focused on returning hostages, as well as considerations for the disarming of Hamas and establishing future governance in Gaza.

The conflict, which began with a significant attack by Hamas on Israel, has resulted in substantial loss of life on both sides.

As negotiations continue without clear advancements, there are growing concerns that a de facto partition of Gaza might emerge, with control split between Israel and Hamas, raising questions about the region's future governance.