He added he would like the fighting to be paused for “as long as prisoners keep coming out.”
The truce between Israel and Hamas entered its final 24 hours Monday, with signs the militant group was willing to extend the pause after it freed more hostages, including a four-year-old girl orphaned by its attack.
Tearful reunions of families and hostages, released in exchange for dozens of Palestinian prisoners, have brought the first relief in the seven-week war.
Militant group Hamas raided Israel on October 7 in the worst attack in the country’s history, prompting devastating Israeli bombardments of the Gaza Strip.
As the latest group of Israeli women and children walked free late Sunday, attention turned to calls for the truce to be extended before its scheduled end at 7:00 am (0500 GMT) on Tuesday.
“That’s our goal, to keep this pause going beyond tomorrow so that we can continue to see more hostages come out and surge more humanitarian relief into those in need in Gaza,” US President Joe Biden said Sunday.
He added he would like the fighting to be paused for “as long as prisoners keep coming out.”
“I get a sense that all the players in the region are looking for a way to end this so the hostages are all released and… Hamas is completely no longer in control of Gaza.”
Hamas has signalled its willingness to extend the truce, with a source telling AFP the group told mediators they were open to prolonging it by “two to four days”.
“The resistance believes it is possible to ensure the release of 20 to 40 Israeli prisoners” in that time, the source close to the movement said.
Hamas has released 39 Israeli hostages and Israel has freed 117 Palestinian prisoners in exchange under the terms of the agreement. A further 19 foreign nationals have also been released from Gaza under separate arrangements.
Under the truce, 50 hostages held by the militants were to be freed over four days in exchange for 150 Palestinian prisoners. A built-in mechanism extends the truce if at least 10 Israeli captives are released each extra day.
Some hostages are believed to be held by militant groups other than Hamas, potentially complicating future releases.
Israel faces pressure from the families of hostages, as well as allies, to extend the truce to secure more releases.
“It would be good, helpful and necessary” to extend the truce until all hostages, who include French nationals, are freed, French Foreign Minister Catherine Colonna told BFMTV on Sunday.
Three successive days of hostage releases have buoyed spirits in Israel, with tearful reunions weeks after Hamas militants poured across the border on October 7, killing 1,200 people, mostly civilians, according to Israeli officials.
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.
The third group of hostages released Sunday included a four-year-old American citizen called Abigail whose parents were both killed in the Hamas attacks.
“What a joy to see her with us. But on the other hand, what a pity that she returns to the reality of not having parents,” Israeli Prime Minister, Benjamin Netanyahu said.
“She has no parents, but she has a whole nation that embraces her,” he added.
Also among those freed Sunday was an 84-year-old woman who was rushed to intensive care in critical condition “after serious neglect”, medical officials said.