Donald Trump has said negotiations over a potential summit with North Korean leader with Kim Jong Un are "going along very well".
The US President said they are still considering the 12 June date for the summit in Singapore.
"We're doing very well in terms of the summit with North Korea," Mr Trump said at the White House.
"It's moving along very nicely. So we're looking at June 12th in Singapore. That hasn't changed. So, we'll see what happens."
Mr Kim believes a summit with Mr Trump will be a landmark opportunity to end decades of confrontation, South Korea's President Moon Jae-in said following his surprise meeting with the North Korean leader.
"He (Kim) also expressed his intention to put an end to the history of war and confrontation through the success of the North-US summit and to co-operate for peace and prosperity," Mr Moon told reporters.
A statement from North Korea's state news agency KCNA said Mr Kim expressed "his fixed will" on the possibility of meeting Mr Trump as previously planned.
A White House team will leave as scheduled for Singapore this weekend to prepare for the possible summit, a White House spokeswoman confirmed.
Mr Kim and Mr Moon held talks in the demilitarised zone separating their two nations on Saturday in a scramble to save the June summit.
Mr Trump had rattled the region on Thursday by cancelling his meeting with Mr Kim, citing "open hostility" from Pyongyang.
But within 24 hours he reversed course, saying it could still go ahead after productive talks were held with North Korean officials.
During his two-hour meeting with Mr Kim, Mr Moon said he urged both Washington and Pyongyang "to remove misunderstandings through direct communication and to have sufficient dialogue in advance through working-level negotiations on the agendas to be agreed upon at the summit".
"Chairman Kim agreed on that," he added.
Pictures from the summit show Mr Moon and Mr Kim shaking hands as well as embracing, and reveal Mr Kim brought along his sister, Kim Yo Jung.
She has played a major public role in talks with the south and led the delegation to the Winter Olympics in February.
Mr Trump's decision to pull the summit is understood to have followed comments from North Korean diplomat Choe Son Hui, who referred to US Vice-President Mike Pence as a "political dummy".
She also said it was up to the Americans whether they would "meet us at a meeting room or encounter us at nuclear-to-nuclear showdown".
The Trump administration is demanding that North Korea completely and irreversibly shutter its nuclear weapons programme.
Mr Kim and Mr Trump's initial decision to meet followed months of war threats and insults between the leaders over the programme.