The US President had fired John Bolton last week, revealing deep divisions between the two on major foreign policy issues including nuclear talks with Pyongyang.

Trump on Thursday said he would consider trying a "new method" in talks with Pyongyang, which have been deadlocked since the collapse of his second summit with Kim Jong Un collapsed in February.

Kim Myong Gil, Pyongyang's top delegate for working-level negotiations with Washington, said the comment underscored a "political perception and disposition peculiar to President Trump", calling it a "wise political decision" in a statement carried by the official Korean Central News Agency.

"At the moment I am not quite sure what he implied in his suggestion of 'new method'," he added.

"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."

Trump had criticised Bolton's suggestion of the "Libyan model" for North Korea, a reference to a denuclearisation deal with the African nation's former dictator Moamer Kadhafi -- who was killed after being deposed in 2011.

Pyongyang had bristled at that comment, which Trump said had "set us very back very badly".

Kim Myong Gil described Bolton as "a nasty trouble-maker who used to face everything out of his anachronistic way of thinking".

North Korea and the United States agreed to restart working-level dialogue during an impromptu meeting between Trump and Kim Jong Un at the Demilitarized Zone dividing the two Koreas in June, and Pyongyang has offered to hold those talks in late September, a move the US has described as "encouraging".

There has been no announcement yet on the venue and precise schedule for the talks.