A ceasefire deal between Israel and Hamas is “closer than we’ve ever been”, according to Joe Biden.
However, speaking at the White House, the US president cautioned an agreement was “not there yet”.
Following two days of talks in Doha, Qatar, senior officials made positive noises about the direction of negotiations.
Negotiators are due to reconvene in Cairo, Egypt, next week to try and finalise the deal.
“I don’t want to jinx anything… we may have something,” Mr Biden told reporters in the White House’s Oval Office.
He added: “But we’re not there yet.
“It’s much, much closer than it was three days ago. So, keep your fingers crossed.”
Mr Biden has previously expressed optimism that an agreement could be reached, only for talks between the parties to break down.
A source with direct knowledge of the talks told Sky News they were “cautiously optimistic” an agreement could be reached.
The deal would see the release of hostages held since the 7 October attacks on southern Israel, in which more than 1,200 people were killed and more than 250 taken hostage.
In retaliation, Israel has waged a military campaign against Hamas in Gaza, a conflict that has so far claimed more than 40,000 lives, according to the Hamas-run health ministry in Gaza.
A joint statement from the White House, Egypt, and Qatar, on Friday, described talks as “serious and constructive and conducted in a positive atmosphere”.
“Senior officials from our governments will reconvene in Cairo before the end of next week with the aim to conclude the deal under the terms put forward today,” they said.
This comes after a village was set ablaze in the West Bank by Israeli settlers, who torched homes with families inside.
Hamas didn’t participate in the most recent talks directly and accused Israel of adding new demands to a previous proposal that they had agreed to in principle.
Both sides previously agreed, in principle, to the plan Mr Biden announced on 31 May.
But, Hamas has proposed amendments and Israel has suggested clarifications – leading to each side accusing the other of trying to tank the deal.
On Friday, mediators said they had presented a proposal to both parties, which they hope will build on areas of agreement and bridge any remaining gaps.
However, Hamas previously cast doubts on whether any agreement was within reach, claiming the latest proposal differed significantly from the previous iteration – raising concerns they were disposed to reject it.
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International diplomacy also intensified on Friday as part of efforts to stop the war from spreading, with the British and French foreign ministers making a joint trip to Israel.
Foreign Secretary David Lammy and French foreign minister Stephane Sejourne appeared hopeful after meeting with Israeli foreign minister Israel Katz.
Mr Katz said in a statement that he had told his British and French counterparts that, if attacked by Iran, Israel expects its allies to help not just defend itself, but in attacking Iran back.