Egypt's state-affiliated Al-Qahera News TV channel also confirmed the arrival of the Hamas delegation in Cairo.
An Egyptian source who spoke to Reuters said, "the results today will be different. We have reached an agreement over many points, and a few points remain."
A Palestinian official with knowledge of the mediation efforts sounded cautious optimism.
"Things look better this time but whether an agreement is on hand would depend on whether Israel has offered what it takes for that to happen," the official, who asked not to be named, said.
The Hamas delegation arrived from the Palestinian Islamist movement's headquarters in Qatar, which along with Egypt, has tried to mediate a follow-up to a brief November cease-fire.
The United States - which, like other Western powers, brands Hamas a terrorist group - has urged it to enter a deal. However, the talks have stumbled over the militant group’s long-standing demand for a commitment to end the almost seven-month-old offensive by Israel.
Israel insists that after any truce it would resume operations designed to disarm and dismantle Hamas.
"Israel will under no circumstances agree to ending the war as part of a deal to free our hostages," an Israeli official said on Saturday, signaling this core position was unchanged.
Hamas said on Friday it would come to Cairo in a "positive spirit" after studying the latest proposal for a deal, little of which has been made public.
Israel has given a preliminary nod to terms which one source said included the return of between 20 and 33 hostages in exchange for the release of hundreds of Palestinian prisoners and a weeks-long suspension of fighting. That would leave around 100 hostages in Gaza, some of whom Israel says have died in captivity.
The source, who asked not to be identified by name or nationality, said their return may require an additional deal with broader Israeli concessions.
"That could entail a de facto, if not formal, end to the war - unless Israel somehow recovers them through force or generates enough military pressure to make Hamas relent," the source said.
Egyptian sources said CIA Director William Burns arrived in Cairo on Friday. He has been involved in previous truce talks and Washington has signaled there may be progress this time.
The CIA declined to comment on Burns' itinerary.
Egypt made a renewed push to revive negotiations late last month after Cairo was alarmed by the prospect of an Israeli assault against Hamas in Rafah in southern Gaza, where more than 1 million Palestinians have taken shelter near the border with the North African nation’s Sinai Peninsula.
A major Israeli operation in Rafah could deal a huge blow to fragile humanitarian operations in Gaza and put many more lives at risk, according to U.N. officials.
Israel says it will not be deterred from taking Rafah eventually and is working on a civilian evacuation plan.
Saturday's Cairo talks come as Qatar reviews its role as mediator, according to an official familiar with Doha's thinking.
Qatar may cease hosting the Hamas political office, said the official, who did not know if, in such a scenario, the Palestinian group's delegates might also be asked to leave.
The war began after Hamas staged a cross-border raid on October 7 in which 1,200 people in southern Israel were killed and 252 hostages taken, according to Israeli tallies.
More than 34,600 Palestinians have been killed, 32 of them in the past 24 hours, and more than 77,000 have been wounded by Israeli fire during a campaign that has laid waste to the coastal enclave, according to Gaza's health ministry.
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