Trump on Thursday was responding to a suggestion made by his National Security Adviser John Bolton a few days back, and said: "The Libyan model is not a model that we have at all, when we're thinking of North Korea."
"This would be with Kim Jong-un -- something where he would be there, he would be in his country, he would be running his country."
Trump, who was scheduled to meet the top leader of North Korea on June 12, however, also cautioned that the Libya model could take place if "we do not most likely make a deal", Xinhua news agency reported.
Gaddafi had given up atomic weapons and was later killed in a US-backed uprising.
Pyongyang on Wednesday responded strongly, saying that the country may reconsider the scheduled Trump-Kim summit because of extremely provocative remarks made by American officials.
North Korea's First Vice Foreign Minister Kim Kye-gwan said in a statement that Bolton had even urged Pyongyang to abandon its nuclear arsenal first in order to receive benefits on trade, a stance similar to that taken with Libya.
"This is not about solving problems through dialogue, but is intended to replay the tragedy of Libya on North Korea," Kim Kye-gwan said, adding that Libya "has totally collapsed after handing over its fate to big powers".
The slated talk almost hit a rough patch earlier this week with Pyongyang saying it was reconsidering the summit.
However, the White House remained somewhat upbeat about the upcoming Trump-Kim summit in Singapore and its Spokesperson Sarah Sanders at a daily briefing on Thursday, said: "Nothing has changed on our end. The President is fully prepared to have the meeting. But if not, that's okay too. And we will see what happens beyond that."
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)