South Korean President Moon Jae-in (File photo: Reuters)

South Korean President Moon Jae-in on Tuesday called the summit between North Korean leader Kim Jong Un and US President Donald Trump a "success."

In a statement, Moon applauded Kim and Trump for their courage and determination to take a daring step towards change.

Moon said the joint statement signed by the two leaders will be recorded as a historic event that would help dissolve the last remaining vestige of the Cold War.

Under the joint statement, Pyongyang and Washington agreed to a complete denuclearization of the Korean Peninsula in exchange for security guarantees for North Korea.

The two countries agreed to establish a new kind of bilateral relations under the joint statement.

Moon said it was a great victory achieved by both the United States and the two Koreas, and a huge step forward for people across the world who long for peace.

The South Korean president also extended his heartfelt appreciation to Singaporean Prime Minister Lee Hsien Loong and other world leaders who helped make the summit a success.

"We will write a new chapter of peace and cooperation leaving the dark days of war and conflict behind," said Moon, who vowed to be there together with North Korea along the way.

Moon said there may be many difficulties ahead as the US-North Korea summit was just a beginning, but noted that South Korea would never give up on this bold journey.

He said history is a record of people who take action and rise to a challenge, noting that his government will spare no effort to ensure that the US-North Korea agreement is implemented in its entirety.