The presidential office says a new process supported by related countries is being introduced with the Pyongyang Declaration which was signed by the leaders of the two Koreas Wednesday.

Senior presidential press secretary Yoon Young-chan told reporters on Thursday a "new time has begun," as he introduced reactions from Washington, Beijing, Moscow and Tokyo on Wednesday's inter-Korean summit.

Yoon cited U.S. President Donald Trump, who said "significant progress" has been made. Trump also revealed that he received a letter from North Korean leader Kim Jong-un three days ago.

Yoon also quoted U.S. Secretary of State Mike Pompeo, who said Washington will engage in talks with Pyongyang “immediately,” with the aim of completing Pyongyang’s denuclearization before Trump’s first term ends in January 2021.

Pompeo added he had requested a meeting with his North Korean counterpart Ri Yong-ho on the sidelines of the UN General Assembly.

Yoon said China assessed the two Koreas have reached a new and significant agreement, Russia expressed support for the two Koreas’ effective move, and Japan hoped the latest agreement would lead to the complete denuclearization of the Korean Peninsula.