Trump said it's been a "tremendous" 24 hours, stepping to the podium to speak with reporters at the press conference.
The president said it's his "honor" to address the people of the world after the summit. Trump said his meeting with Kim was honest, direct and productive.
The president said US sanctions on Korea would remain for now.
Trump said Kim told him North Korea is destroying a nuclear site and is already destroying a "major" missile testing site. The president claimed that agreement came after the two signed the document and is not in the document.
"The past does not have to define the future," Trump said, suggesting that the two nations need not be enemies.
Trump claimed that, this time, it won't be like past administrations' attempts to deal with North Korea.
Human rights violations were discussed with Kim Jong-un, says Trump. The remains of the thousands of prisoners of war who died in the Korean war of 1950 will be repatriated. "He is very smart. A very good negotiator," says Trump.
"Will travel to Pyongyang and will invite Kim Jong-un to the White House at the appropriate time," Trump said.
The US president said 32,000 US soldiers were in South Korea and it was time to bring them home. "Will be stopping the war games which will save the US a tremendous amount of money," he said.
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