New South Korean President Moon Jae-in will visit the White House next month for a summit with President Donald Trump amid worries over North Korea's progress in building a nuclear and missile arsenal.

The agreement for the leaders to meet in late June followed a meeting in Seoul between Chung Eui-yong, Moon's foreign policy adviser, and Matt Pottinger, US National Security Council director for East Asia, said Moon's spokesman Yoon Young-chan.

Tuesday's announcement came days after North Korea successfully tested a powerful new missile that analysts believe could reach Alaska when perfected.

Yoon said Chung and Pottinger in their meeting reaffirmed that Seoul and Washington shares a common goal in the "complete discarding" of North Korean nuclear weapons and will pursue "all methods, including sanctions and dialogue" to reach the goal.

The allies agreed that dialogue with North Korea could happen under the "right conditions," he said.

A date and other specifics of the summit are still to be decided, Yoon said.

"We will prepare the summit meeting so it could serve as an opportunity for both leaders to develop their personal bond and friendship."

Liberal South Korean President Moon Jae-in favours a softer approach to North Korea than his conservative predecessors and has offered to visit Pyongyang if the circumstances are right.

But Washington is Seoul's closest ally and military protector, and the North's rising nuclear and missile tests make close co-ordination crucial.