On Thursday evening, The New York Times reported Trump had ordered the Pentagon to develop plans for reducing troop levels in South Korea.
Earlier Friday, National Security Adviser John Bolton called the Times report "utter nonsense".
He denied that he had requested the Pentagon to draw up options for withdrawing troops from South Korea.
And in another sign of the times, North Korea announced on May 4 that it had moved its clock ahead by 30 minutes to align itself with South Korea's time zone.
The meeting between North Korean leader Kim Jong Un and South Korean President Moon Jae-in was short of specifics and failed to clear up the question of whether Pyongyang is really willing to give up nuclear missiles that now threaten the United States.
KCNA earlier said Kim proposed returning North Korea to the South's time zone because it was "a painful wrench to see two clocks indicating Pyongyang and Seoul times hanging on a wall of the summit venue".
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It wasn't immediately clear when the location or date would be publicly revealed.
"Now I have to tell you, at some point into the future, I would like to save the money", Trump said later as he prepared to board Air Force One. But I think a lot of great things will happen.
But the rapidly evolving peace process with the North has led to suggestions that US troops might not be needed if a treaty is signed. "South and North Korea shared the view that the measures being initiated by North Korea are very meaningful and crucial for the denuclearization of the Korean Peninsula and agreed to carry out their respective roles and responsibilities in this regard", the two leaders wrote in a joint statement. Under the current agreement that expires at the end of 2018, the South provides about $830 million per year.
"We're having very substantive talks with North Korea", Trump said.
President Trump did not share details on the time and place for the landmark meeting with Mr Kim. "Stay tuned!" Trump stated via his Twitter social media account.