Trump did not refer to the document as a treaty or agreement.
"We're starting that process very quickly".
The world was watching as they smiled for the cameras, then sat down to make brief remarks before going into a almost 40-minute private meeting, with only translators present.
"I think both sides are going to be very impressed with the result", he said.
He appeared on television wearing a Trump supporters' "Make America Great Again" hat and a tee-shirt from his cryptocurrency sponsor. While the Air Force One carrying Donald Trump landed in Singapore on Sunday evening, Kim Jong-un reportedly travelled by a Chinese plane, deployed for his personal use, and was received by Singaporean foreign minister. A North Korean aide wearing latex gloves reportedly inspected and wiped the pen intended for Kim, which he didn't end up using.
Ms Leong added both found it hard to hide their nervousness once they were seated, with Trump displaying a slanted smile, and fidgeting with his hands and Kim leaning and staring at the ground. They then resumed their walk.
"I feel really great". Kim described the meeting as "a good prelude to peace". "Good relationship", said Trump to reporters during a break. "I don't say he was nice".
The dollar jumped to a 3-week top on Tuesday and Asian shares rose on the news.
Mr Trump's delegation at the luncheon included US National Security Adviser John Bolton, Secretary of State Mike Pompeo, White House Chief of Staff John Kelly and Press Secretary Sarah Huckabee Sanders.
The two leaders met for about 40 minutes and were joined only by interpreters.
As the two flags hung side-by-side in the backdrop for the first time ever, both Kim and Trump expressed hope that their summit would be fruitful.
Professor Hajek added Trump showed his experience in front of the TV cameras during the initial meeting.
-North Korea summit, is expected to pick up a considerable portion of North Korean leader Kim Jong-un's bills.
Singapore is one of the few countries that have diplomatic relations with both the U.S. and North Korea.
But North Korea's complete denuclearization is "the only outcome that the United States will accept", Pompeo said, and sanctions will not be lifted until that happens.
"If diplomacy does not move in the right direction, those measures will increase", he said.