Sullivan said Biden should also speak with Egyptian President Abdel Fattah al-Sisi.
The latest developments come as Netanyahu faces fierce opposition to a potential deal from his ruling coalition. Ten right-wing members, including some from Netanyahu’s own Likud party, sent him a letter opposing the truce.
A Palestinian official told the BBC that Hamas and Israeli officials held indirect talks in the same building on Monday.
Revealing some of the possible details of the agreement, the official said that “detailed technical discussions took a long time.”
Both sides agreed that Hamas would release the three hostages on the first day of the agreement, after which Israel would begin withdrawing troops from the settlements.
In seven days, Hamas will release four more hostages, and Israel will allow displaced persons from the south to return to the north, but only on foot along the coastal road. Cars, animal carts and trucks will be allowed to pass through the road adjacent to Salah al-Din Road under the supervision of an X-ray machine operated by a Qatari-Egyptian technical security team.
The agreement includes provisions for Israeli forces to remain in the The Philadelphia Corridor and maintain an 800-meter buffer zone along the eastern and northern borders during the first phase, which will last 42 days.
Israel also agreed to release 1,000 Palestinian prisoners, including about 190 who were serving sentences of 15 years or more. In exchange, Hamas will release 34 hostages.
Negotiations on the second and third stages of the agreement will begin on the 16th day of the ceasefire.
Meanwhile, the Gaza Civil Defense Agency reported that more than 50 people were killed in a wave of Israeli airstrikes in Gaza City on Monday.
“They bombed schools, houses and even people’s gatherings,” civil defense spokesman Mahmoud Basal told AFP.
The Israeli military said it was investigating the reports. Separately, it said five soldiers were killed on Monday in the northern Gaza Strip.
The war was sparked by a Hamas attack on southern Israel on October 7, 2023, which killed around 1,200 people and took 251 hostages in Gaza.
In response, Israel launched a military operation in Gaza to destroy Hamas.
The Hamas-run Gaza Health Ministry says more than 46,500 people have died during the war.
Israel says 94 hostages remain in Gaza, 34 of whom are presumed dead, along with four other Israelis abducted before the war, two of whom are dead.