Kim Myong Gil praised Trump's "wise political decision" to seek a new approach to the stalled talks without a "troublemaker" in the U.S. administration - an apparent reference to John Bolton, Trump's hawkish former national security adviser, who was fired last week.
Trump said on Wednesday Bolton's suggestion for a Libyan model of denuclearization for North Korea "set us back very badly," while his own diplomacy had resulted in the country freezing nuclear tests and returning remains of U.S. soldiers missing from the 1950-53 Korean War.
"So I think John really should take a look at how badly they've done in the past and maybe a new method would be very good," Trump said, when asked about news reports saying that Bolton thought talks with North Korea were doomed to failure.
Kim Myong Gil said he wanted to be "optimistic" that the United States would present the "right calculation method at the upcoming talks," an apparent reference to a call by North Korean leader Kim Jong Un for Washington to show more flexibility.
"At the moment I am not quite sure what he (Trump) implied in his suggestion of 'new method' but to me it seems he wanted to imply that a step-by-step solution starting with the things feasible first while building trust in each other would be the best option," Kim added in a statement carried by North Korea's official KCNA news agency.
The White House did not respond when asked to elaborate on Trump's remarks.
The State Department repeated a past statement, saying: "We welcome the North Korean commitment to resume negotiations in late September. We are prepared to have those discussions at a time and place to be agreed."
It did not respond when asked if there could be any contacts with the North Koreans on the sidelines of next week's United Nations General Assembly in New York, which Trump and Secretary of State Mike Pompeo are due to attend.
North Korea's mission to the United Nations said early this month that the country's foreign minister, Ri Yong Ho, would not attend the annual gathering of world leaders "due to his schedule."
Trump's efforts to engage with North Korea nearly fell apart in February after he followed Bolton's advice at a second summit in Hanoi and handed Kim Jong Un a piece of paper urging Pyongyang to transfer all of its nuclear weapons and bomb fuel to the United States.
Pyongyang has denounced Bolton, who has advocated using military force to topple the leadership of the isolated country, as a "war maniac" and "human scum."
While negotiations have stalled since Hanoi, North Korea said this month that it was willing to restart working-level talks in late September, but no date or location have been set.
The KCNA statement formally confirmed Kim Myong Gil as North Korea's new chief negotiator, after diplomatic sources told Reuters in July that he would act as counterpart to U.S. Special Representative for North Korea Stephen Biegun.