After a working lunch concluded a morning of negotiations in Singapore, the US president said a lot of progress had been made as they tried to “solve” the Korean Peninsula stand-off.
Asked about the discussions, he said: "A really fantastic meeting - a lot of progress. Better than anybody could have expected."
Trump added: "We are going right now for a signing".
Before lunch, he hailed his “excellent” relationship with Mr Kim and predicted the pair will “solve” the Korean Peninsula stand-off after their historic meeting.
The US president said his one-on-one meeting with the North Korean leader, which lasted around 40 minutes, was “very good” and predicted “tremendous success”.
The comments came after the two leaders shared a 12-second handshake as they met for the first time in front of a dozen American and North Korean flags.
Trump patted Kim on the arm and shared some words before the pair turned and posed for the cameras in Singapore.
The White House says that the United States' delegation at the larger meeting will include Secretary of State Mike Pompeo, White House chief of staff John Kelly, and National Security Adviser John Bolton.
Meanwhile, after some initial exchanges lasting around 40 minutes, Trump and 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.
Trump's threats to politely walk out of the meeting if his expectations were unmet did not materialize.
US President Donald Trump and North Korean leader Kim Jong Un have met for the first time in Singapore, shaking hands against the backdrop of U.S. and North Korean flags level and side-by-side.
The summit announcement came in March after several months of unprecedented cordial diplomacy between South and North Koreas, which had been adversaries for decades.
