The United States wants swift and irreversible denuclearisation, while North Korea has made clear it wants phased, synchronized and reciprocal actions that would include easing punishing sanctions.
Sanders praised North Korea's efforts to reconcile but ruled out, for now, a key demand of Pyongyang - a lifting of sanctions.
U.N. Secretary-General Antonio Guterres said "it's high time" for serious negotiations between the United States and North Korea to outline a roadmap for the denuclearization of the Korean peninsula.
She was referring to Pyongyang's quick deportation past year of an American.
The U.S. and North Korea seemed close to war at points during 2017.
Last week, South Korean President Moon Jae-In urged Pyongyang to take "bold, practical measures for denuclearisation" to ensure sanctions are lifted but stressed that "corresponding measures" were also needed from Washington, such as agreeing a "peace regime" and formally declaring an end to the 1950-1953 Korean War. Some critics say the first summit only boosted Kim's global stature without much to show for it.
Nevertheless, both he and Mr. Trump had expressed an interest in arranging a second meeting, something some US -based analysts see as premature.
Sanders told reporters the President's intention for keeping the Speaker and other lawmakers in the country over the weekend is to make sure progress is made on the government shutdown front, so that government workers can receive their paychecks as swiftly as possible.
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"I don't think we have any concrete agreement", said Sue Mi Terry, a former Central Intelligence Agency analyst who's now at the Center for global and Strategic Studies in Washington.
'If (the US) is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea, ' he said.
Barring any last-minute diplomatic tussles between Kim Yong Chol and the White House as his visit to Washington wraps up, Biegun is expected to travel to Stockholm to meet Choe on Sunday, according to a South Korean official.
Kim Yong Chol met with Secretary of State Mike Pompeo earlier Friday at a DC hotel before heading to the White House.
The summit was announced even though there has been no indication of any narrowing of differences over USA demands that North Korea abandon a nuclear weapons program that threatens the United States and Pyongyang's demands for a lifting of punishing sanctions.
They say the North Koreans are holding out for a second summit because they believe they can extract greater concessions by meeting with Trump directly, as opposed to working with envoys like Pompeo or Biegun.
Since then, several private analysts have published reports detailing continuing North Korean development of nuclear and missile technology.
Trump declared after the Singapore summit in June that the nuclear threat posed by North Korea was over. Kim, whose family has ruled North Korea with an iron fist for three generations, is seeking guarantees of the regime's survival as well as relief from biting United Nations sanctions.