Kushner will meet with Israel's prime minister on Monday. The talks aim to salvage the new 15-point, US-backed road map for Hamas to disarm in Gaza and Israel to withdraw from the Palestinian territory shattered by war.
At stake are the lives of some two million people in Gaza and the reconstruction of the crowded enclave now largely controlled by Israeli forces, more than 10 months since the ceasefire ended major military operations.
A meeting between Kushner, fellow envoy Steve Witkoff and Hamas leaders in Egypt last year helped clinch the ceasefire, whose progress until now had been stalled over the key issue of Hamas' disarmament.
The rare meeting in Egypt with Hamas' Khalil al-Hayya was confirmed by a regional official and a Hamas official, both speaking on condition of anonymity because they were not authorised to talk to reporters.
Kushner was one of a trio of envoys meeting with al-Hayya, with officials from mediating countries Egypt, Qatar and Turkey also attending.
Israeli Prime Minister Benjamin Netanyahu last week rejected the 15-point plan in a rare public show of defiance against the Trump administration, Israel's closest ally.
Now Kushner, former British prime minister Tony Blair and the director of the US-created Board of Peace overseeing the ceasefire, Nickolay Mladenov, are set to meet with Netanyahu on Monday.
Ahead of Monday's meeting with Netanyahu, several regional powers including Saudi Arabia and the United Arab Emirates issued a statement condemning Israel's rejection of the road map, saying that: "Israel now bears responsibility for obstructing the efforts to bring peace in Gaza".
Other signers included Jordan, Pakistan, Indonesia and the ceasefire mediators.
The statement by foreign ministers also called on the Board of Peace and the US to take "immediate and concrete measures" to keep any party from obstructing the plan's implementation.
Kushner's meeting with the Hamas leader aimed at ensuring the militant group's commitment to the road map, particularly disarmament, before his meeting with Netanyahu, the regional official said.
The Hamas official said the group is committed and waiting for mediators to start the 14-day negotiation period to work out a timetable for the implementation. That period requires all parties' approval of the road map to begin.
The Hamas official also said the Hamas leader demanded that Israel halt its attacks on Gaza and withdraw to the so-called "yellow line" dividing the territory before beginning implementation of the road map.
The yellow line was never precisely defined. Israeli forces have moved beyond it and now control about 60 per cent of Gaza.
In May, Netanyahu said the next step was to move to 70 per cent control, with Israel "tightening the grip" on Hamas "from every direction".
Under the road map, Hamas would hand over weapons to the Palestinian technocratic committee meant to oversee daily operations in the territory.
The committee has not yet entered Gaza. But Hamas has linked the surrender of its heaviest weapons to the creation of a Palestinian state, something Israel's current government rejects.
The road map involves Hamas gradually giving up its weapons while Israeli forces halt attacks and begin withdrawing from Gaza. But Netanyahu says Israel will not retreat from any position in Gaza until Hamas has been completely disarmed.
That stance leaves other elements of the ceasefire, including reconstruction and the deployment of international forces to separate Israeli forces from committee-controlled areas, on hold.
