US president Donald Trump has signed three agreements with North Korea leader Kim Jong-un at a summit in Singapore today, but what is in them remains a mystery.
Mr Trump said the pair had made "a lot of progress".
Asked by reporters how the talks were going, Mr Trump said: "A lot of progress - really very positive. I think better than anybody could have expected. Top of the line, very good. We're going now for a signing."
He gave no further details.
Mr Trump made the remarks as he and Mr Kim walked around Singapore's Capella hotel after a working lunch aimed at discussing ways to end the nuclear standoff on the Korean peninsula.
Earlier the two leaders shook hands and posed for photographs, before moving inside the hotel to talk to reporters.
Watch a live feed of the meeting here:
Mr Trump said he felt "really great" about the meeting.
"We're going to have a great discussion and I think tremendous success. It will be tremendously successful. And it's my honour and we will have a terrific relationship I have no doubt."
Speaking through his translator, Mr Kim said it was "not easy" to get here.
"The past... and the old prejudices and practices worked as obstacles on our way forward. But we overcame all of them and we are here today."
Both men looked serious as they got out of their limousines for the summit at the Capella hotel on Singapore's Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
But they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters. Mr Trump had said on Saturday he would know within a minute of meeting Mr Kim whether he would reach a deal.
After some initial exchanges lasting about half an hour, Mr Trump and Mr Kim emerged, walking side-by-side through the colonnaded hotel before re-entering the meeting room, where they were joined by their most senior officials.
The talks - unimaginable just a few months ago - will focus on North Korea's controversial nuclear programme.
It is the first time a sitting US president has ever met a North Korean leader.
Shortly before the summit began, Mr Trump tweeted that his top economic adviser, Larry Kudlow, had suffered a heart attack and was in hospital.
Our Great Larry Kudlow, who has been working so hard on trade and the economy, has just suffered a heart attack. He is now in Walter Reed Medical Center.— Donald J. Trump (@realDonaldTrump) June 12, 2018
Mr Trump said earlier the highly anticipated talks represent a "one-time shot" at peace.
The summit is being held at a hotel on Sentosa, a popular tourist island a few hundred metres off the Singapore mainland and started at 1pm.
Details of the agenda have been released. According to the White House, this is the plan for the summit:
- Mr Trump and Mr Kim initial greetings (9am local time; 1pm NZT)
- One-to-one meeting
- Expanded meeting with other representatives
- Working lunch
Mr Trump will leave the country that same evening to return to the US. Mr Kim is reported to be flying out even earlier, at 14:00 local time (6pm NZT).
- RNZ / BBC