Ambassador Cho Yoon-je said both leaders have shown a commitment to having a second summit, including in Kim's New Year's address.
"The train is already on the move and no one wants to jump off the train," Cho said at a discussion hosted by the Hudson Institute, alluding to the brisk diplomatic engagement with Pyongyang that began last year.
"The question is how fast and how far the train can move, but I don't think it will be stopped or reversed, at least in the near future," he said.
Trump and Kim held their first summit in Singapore in June and agreed to work toward the complete denuclearization of the Korean Peninsula in exchange for security guarantees from the US.
The process has stalled as the sides have sparred over the exact terms of the deal, including how far the North will have to dismantle its nuclear weapons program before receiving sanctions relief from the US.
"I think once we are on the train and the train is on the move, we have to make theater and we have to make progress," Cho said.
He added that Kim's visit to China this week was "quite a good sign" that the second summit will happen. The North Korean leader met with Chinese President Xi Jinping, as he did ahead of his first summits with South Korean President Moon Jae-in and Trump last year.
"I expect the second summit between Mr. Trump and Chairman Kim will take place. When? I do not know. I guess the communication is going on now," Cho said.
The ambassador addressed concerns that North Korea may be driving a wedge in the Seoul-Washington alliance by pursuing cross-border projects with the South on the one hand and dragging out denuclearization talks with the US on the other.
He said the "inter-Korean peace process," which has included reconnecting railways and roads, can "create trust that can make Pyongyang feel more secure and comfortable to take the next step toward denuclearization."
And the alliance, he said, has been resilient over the years.
"We may sometimes have different views and approaches to problems, but through constructive debates and close consultation, we have always sought the best approach for the alliance," Cho said. "I am sure even Pyongyang would not expect any less."
It was in the spirit of the alliance that Seoul accepted most of Washington's demands related to the auto sector when they amended their bilateral free trade agreement last year, he said when asked about the US' possible introduction of tariffs on imported cars.
"To be frank, we don't think it makes much sense if it's applied to Korea because we accommodated most of the demands of the US side on the automobile sector," Cho said. "We hope Korea would not be subject to that Section 232."
The US Department of Commerce is due to submit a report to Trump in mid-February on its investigation into whether to slap tariffs on imported cars and parts on national security grounds, under Section 232 of the Trade Expansion Act.
Trump will then have 90 days to make a final decision. (Yonhap)