The source added that the delegations conducted negotiations in Cairo since the morning and that progress has been made despite some remaining controversial points.
Addressing all participating parties, the Egyptian security delegation stressed the danger of escalation and eschewing the path of negotiations.
The delegation also highlighted Egypt's efforts to maintain the negotiations.
Earlier, a high-level Egyptian source told Al-Ghad TV channel that the Israeli delegation attempted to raise other controversial points during the talks before the Egyptian, Qatari, and American mediators.
Israel, he explained, opposed a particular clause in the agreement concerning Hamas' release of 33 detainees regardless of their condition, insisting, on the other hand, that the 33 detainees meet certain criteria.
According to these criteria, the released detainees should be alive and should include women, children, the elderly, and female soldiers belonging to specific age groups.
Israel also insisted on reducing the number of Palestinians released per Israeli captives.
The source further explained that while Hamas proposed releasing three detainees weekly, Israel demanded daily releases.
Reuters reported, citing two Egyptian sources, that the current round of Cairo talks started on Tuesday, with all five delegations reacting positively to the resumption of negotiations.
Mediators from Egypt, Qatar, and the US are strongly pushing for a deal that achieves a cessation of Israeli attacks in Gaza and facilitates exchanging dozens of captives still held by Hamas.
Since the war began on 7 October, Israeli occupation forces have killed 34,844 people, injured 78,404, caused extensive damage to Gaza's infrastructure, and displaced most of the strip’s residents.
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