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.

The Israeli government contends that any negotiations will ultimately focus on disarming Hamas, preventing its return to governance, and ideally establishing a stable path for the future of Gaza.

Since the escalation of the conflict triggered by the Hamas-led attack on southern Israel on October 7, a ceasefire has yet to solidify all parties' commitments effectively, further complicating international attempts for mediation.

The ongoing violence has led to substantial humanitarian crises in Gaza, exacerbating tensions and underscoring the urgency for productive dialogue amid these critical challenges.