The current truce between the warring parties is scheduled to expire early Thursday after a six-day pause in the conflict, sparked by deadly Hamas attacks that prompted a devastating Israeli military offensive in the Gaza Strip.
With 60 Israeli hostages and 180 Palestinian prisoners already released and more set to walk free on Wednesday under the agreement, Qatari mediators said they were working for a "sustainable" cease-fire.
Speaking on condition of anonymity, a source close to Hamas said the militant group on Wednesday "informed the mediators that it is willing to extend the truce for four days."
Under that arrangement, "the movement would be able to release Israeli prisoners that it, other resistance movements and other parties hold during this period, according to the terms of the existing truce," the source added.
Qatar's foreign ministry spokesman Majed Al Ansari told a Doha news conference on Tuesday that negotiators were seeking "a sustainable truce that will lead to further negotiations and eventually to an end... to this war."
A source with knowledge of the talks added in comments to AFP on Wednesday that discussions were "focused on building on the progress of the extended humanitarian pause agreement and to initiate further discussions about the next phase of a potential deal."
After a 48-hour extension of an initial four-day truce, a new group of 12 hostages was freed from Gaza on Tuesday, with 30 Palestinians released by Israel.
An AFP journalist saw masked and armed fighters from Hamas and the Islamic Jihad handing over hostages to Red Cross officials in Rafah, near the border with Egypt.
The Israeli hostages freed were all women, including 17-year-old Mia Leimberg, who returned to the Middle Eastern nation with her mother and aunt. The three were all abducted from kibbutz Nir Yitzhak, and the teenager was seen after her release holding her dog Bella.
The grandmother of 12-year-old Eitan Yahalomi, who was released on Monday, said the boy had been held in solitary confinement for 16 days.
"The days that he was alone were horrible," Esther Yaeli told Israeli news website Walla. "Now Eitan appears very withdrawn."
Hamas has also released a Russian-Israeli, 20 Thais and one Filipino outside the scope of the agreement.
Thailand's foreign ministry said 17 of the released Thai hostages would arrive back in the kingdom on Thursday. It said about 13 Thais remained among the hostages held in Gaza.
Among the Palestinian prisoners freed in Tuesday's exchange was 14-year-old Ahmad Salaima who returned to his home in east Jerusalem to cheers and hugs from relatives.
"When Ahmed was in prison, we couldn't visit him, even though he's the youngest Palestinian prisoner," his father Nayef said.
Israel's government has received a list of the new hostages to be freed Wednesday, Israeli media reported. There was no official confirmation.