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

Hamas has demanded safe passage for the fighters, which has been rejected by Israel. The Israeli government has stated that discussions are centred around the ongoing return of hostages and the disarming of Hamas.

The war in Gaza was triggered by the Hamas-led attack on southern Israel on 7 October 2023, resulting in a significant loss of life and ongoing hostilities. The complex humanitarian and military landscape in Gaza complicates peace negotiations, as both parties accuse one another of violations of any ceasefire agreements.