"Our relationship... I think it remains good," Trump told reporters at the White House, after the Hanoi meeting ended without any agreement on walking back Pyongyang's nuclear program in exchange for sanctions relief.

North Korea's state media earlier acknowledged for the first time the collapse of the high-stakes summit, which was supposed to build on the leaders' historic first meeting in Singapore last year.

"The public at home and abroad... are feeling regretful, blaming the US for the summit that ended without an agreement," an editorial published by Pyongyang's official news agency KCNA said.

Following the stalemate in Hanoi, researchers said this week that Pyongyang had started rebuilding the Sohae long-range rocket site after Kim had agreed last year to shut it as part of confidence-building measures.

Trump said he would be "very, very disappointed" if the reports proved true.