Kim made the remarks during his visit with South Korean Foreign Minister Kang Kyung-wha. His delegation held talks with the North's team, led by Pyongyang's Vice Foreign Minister, Choe Son-hui, in the border truce village of Panmujom, on Sunday and Wednesday.

"As both President Trump and Secretary (of State) Pompeo indicated, there’s much work left before the proposed summit," Kim said.

"We believe that we're moving in the right direction to the ongoing series of consultations, including Secretary Pompeo’s engagement with Vice Chairman Kim Yong-chol ... our discussions at Panmunjom and of course the discussions in Singapore as well," he added.

Over the last week, Washington and Pyongyang have held a series of talks to prepare for the summit, including in Singapore and New York.

Kim called the current juncture of brisk diplomacy a "very important moment" on the peninsula.

"The recent developments between the two Koreas and the proposed summit between President Trump and Chairman Kim, of course, offer a historic opportunity to achieve lasting peace and complete denuclearization," he said.

Kang also depicted the current moment as "truly an important period."

"I think absolutely we’re on the same page," she said.

Kim's delegation reportedly discussed with the North key agenda items for the prospective summit, while on a separate track in Singapore, the two sides discussed security and logistics.

In New York this week, Kim Yong-chol, a vice central committee chairman of the North's ruling Workers' Party, met Secretary Mike Pompeo, apparently to finalize details about the summit.

Washington and Pyongyang are trying to salvage the summit, which was on the verge of collapse last Thursday when Trump walked away, citing "open hostility" from the North. Following the North's conciliatory gesture, Trump later suggested that the summit could happen as planned. (Yonhap)