Talks to strike a provisional agreement on Iran’s nuclear programme are in the “final phase”, the French foreign minister believes.
Laurent Fabius was among a number of negotiators at the Vienna talks expressing hopes for a historic deal.
The agreement would impose limits on Iran’s nuclear programme in return for relief from economic sanctions.
Iranian Foreign Minister Javad Zarif said talks would not be extended beyond Monday, but there was still work to do.
US Secretary of State John Kerry also warned that “major issues” remained, but said he was hopeful.
Mr Fabius, who cancelled a trip to Africa to stay at the talks, said: “I hope we are finally entering the final phase of these marathon negotiations. I believe it.”
A German government source said it was still possible for the negotiations to fail but a deal could be reached quickly if Tehran was ready to take the final steps.
“Negotiations are currently in the absolute final phase and are running intensely through the night,” the source, quoted by Reuters, said.
On Sunday afternoon, two diplomats at the talks said details of the deal were still being worked out and that it would still need to be reviewed by Iran and the so-called P5+1 – the US, UK, Russia, France, China and Germany.
But then the agreement could be announced on Monday.
One remaining task was to re-read the whole document, which spans 100 pages, an Iranian diplomat told AFP news agency.
“Sometimes a country demands that we change a word, sparking several hours of discussions because the meaning can change completely,” he said.
Later on Sunday, a top US state department official cautioned: “We have never speculated about the timing of anything during these negotiations, and we’re certainly not going to start now – especially given the fact that major issues remain to be resolved in these talks.”
An Iranian official was also quoted by the Isna agency as saying that it would be “logistically impossible” to reach a deal on Sunday and that “hard work continues”.
And the top Republican in the US Senate, questioned whether President Barack Obama would then be able to win approval in Congress.
Mitch McConnell told Fox News Sunday: “I think it’s going to be a very hard sell, if it’s completed, in Congress.
“We already know it’s going to leave Iran as a threshold nuclear state.”
The failure to reach an agreement by last Friday means the US Congress will now take twice as long – 60 days – to decide whether to accept or reject any eventual deal, keeping sanctions in place until then.
Western powers suspect Iran of seeking nuclear weapons, but Iran says its programme is for purely peaceful purposes.
The sides have been holding marathon negotiations to reach a long-term agreement and have missed successive self-imposed deadlines.
The main sticking points for the P5+1 and Iran have been international inspections of Iran’s non-nuclear sites, sanctions relief and how Iran’s compliance will be verified.
Iran also wants a UN Security Council arms embargo to be scrapped – something the US has ruled out.