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 mentioned that an amnesty could be offered for fighters who laid down their arms, indicating a potential framework for future negotiations.

Amnesty has gained attention amidst fears of further military confrontations and a potential partition of Gaza, leading to Arab nations expressing concern about the future of Palestinian governance.

The initial ceasefire phase focused on stopping hostilities and returning hostages, but ongoing conflicts raise questions about the next steps. The separation between areas controlled by Hamas and Israel may lead to permanent divisions if not addressed promptly, with each side accusing the other of violating the truce.