A source close to Hamas said the group was willing to prolong the pause.
Hamas released a third group of hostages including a four-year-old American girl Sunday, in exchange for Palestinian prisoners on day three of a truce which a source close to the Hamas said they were willing to prolong.
The transfers under a four-day truce that started Friday have been the first relief for captives' families since the Hamas group attacked Israel on October 7, prompting devastating Israeli bombardments of the Gaza Strip.
Israeli officials said 17 hostages were back on Israeli territory after the latest release. One, in her 80s, was admitted to hospital which said her life was in danger.
US President Joe Biden announced that among those freed is a four-year-old American girl.
"She's been through a terrible trauma," Biden said of Abigail, whose parents were murdered by Hamas during the unprecedented attacks.
The 17 hostages, including three Thai nationals, were released outside the terms of the truce.
Hamas said a Russian-Israeli, Ron Krivoy, was freed "in response to the efforts of Russian President Vladimir Putin" and his "support of the Palestinian cause".
Those released were among around 240 people captured on October 7 when Hamas fighters broke through Gaza's militarised border with Israel in the country's deadliest attack.
The Hamas operatives killed about 1,200 Israelis and foreigners, according to Israeli authorities.
In response, Israel launched a military campaign to destroy Hamas, killing nearly 15,000 people, mostly civilians and including thousands of children, according to Gaza's Hamas government.
Sunday's releases bring the total number of Israelis freed under the deal to 39 since Friday.
In exchange, a further 39 Palestinian prisoners were freed on Sunday, the Israeli prison service said, after the release of 78 other Palestinian inmates from Israeli jails over the past two days.
On Friday Hamas released 10 other Thais and a Filipino, in a surprise move separate from the main deal.
The group's armed wing released a video on Sunday evening showing hostages entering vehicles and then getting off in central Gaza City, devastated by Israel's air and ground offensive, where a crowd hailed the Hamas fighters.
Mounting pressure
Israel has faced mounting pressure to extend the pause mediated by Qatar, the United States and Egypt.
On Sunday, French Foreign Minister Catherine Colonna told BFMTV that "it would be good, helpful and necessary" to extend the truce until all hostages, who include French nationals, are freed.
Biden expressed a similar hope "so that we can continue to see more hostages come out and surge more humanitarian relief into those in need in Gaza".
A source close to Hamas said the group was willing to prolong the pause.
"Hamas informed the mediators that the resistance movements were willing to extend the current truce by two to four days," the source told AFP.
"The resistance believes it is possible to ensure the release of 20 to 40 Israeli prisoners" in that time.
Under the truce, 50 hostages held by Hamas are to be freed over four days in exchange for 150 Palestinian prisoners. A built-in mechanism extends it if at least 10 Israeli captives are released each day.
Israeli leaders, however, have tempered hopes of a lasting halt to the offensive.
"We continue until the end -- until victory," Prime Minister Benjamin Netanyahu said in Gaza on Sunday.
Wearing green military fatigues and surrounded by soldiers, he vowed to free all the hostages and "eliminate Hamas", in footage posted online by his office.
He spoke while making the first visit to Gaza by an Israeli premier since 2005.
"Nothing will stop us, and we are convinced that we have the power, the strength, the will and the determination to achieve all the war's goals," Netanyahu said.
In the southern Gaza city of Khan Yunis, residents received a text message from Israeli forces that said they know hostages are being held there.
"The army will neutralise anyone who has kidnapped hostages," the message said.
'That's enough'
Elsewhere in Gaza, following weeks of bombardment, residents ventured back to pick through heaps of rubble where they once lived.
"I came to see if there was anything left, if there was anything I could salvage. We fled with nothing," said Oussama al Bass, inspecting the ruins of his home in Al-Zahra, south of Gaza City.
"Everything is lost," he said. "We're tired. That's enough. We can't take it anymore."
On the outskirts of Gaza City, families took to the road on foot to head south, pushing luggage and relatives in wheelchairs, and carrying children in their arms.
Among the Israelis freed Sunday was Elma Avraham, 84, who was being treated at Soroka Medical Center, whose director Shlomi Kodesh said "she is in life-threatening condition" but being treated and would be moved to the intensive care unit.
Also freed were sisters Ely, aged eight, and her sister Dafna, 15, whose father was shot dead during the Hamas attack.
In the previous round of releases, there were smiles, kisses, and tears as Israeli hostage Sharon Avigdori, freed with her daughter Noam, 12, hugged her son and relatives at Sheba hospital, images from the government press office showed.
On Sunday in Ramallah and Beitunia, in the Israeli-occupied West Bank, white International Committee of the Red Cross buses delivered the freed prisoners as waiting crowds flew Hamas and Palestinian flags.
Noorhan Awad, a female prisoner released Saturday, said that when she got out of the police car, "it was a great moment. Freedom is priceless."
Hamas's military wing, the Ezzedine al-Qassam Brigades, said Sunday that its northern brigade commander Ahmed Al-Ghandour and four other senior leaders had been killed, without specifying when.
The pause in fighting has allowed more aid to reach Palestinians struggling to survive with shortages of water and other essentials, but Adnan Abu Hasna, a spokesman for the UN agency for Palestinian refugees (UNRWA), warned of "unprecedented" humanitarian needs.
"We should send 200 lorries a day continuously for at least two months," he said.
The UN estimates that 1.7 million of Gaza's 2.4 million people have been displaced by the fighting.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
