SEOUL (REUTERS) - South Korean President Moon Jae-in will clear a top item off his bucket list on Thursday (Sept 20): Climbing Mount Baekdu in North Korea with its leader Kim Jong Un.

After the two leaders pledged new steps aimed at salvaging nuclear talks, South Korea made a surprise announcement that Mr Moon and Mr Kim would use the final day of their three-day summit to go up the symbolic mountain together.

The leaders, accompanied by their wives, reached the Cheonji crater lake on top of Mount Baekdu at around 10.20 am local time (9.20am Singapore time).

Mr Moon is known for his love of mountain climbing and has trekked in the Himalayas at least twice. The 65-year-old president has long stated that he would love to one day visit Mount Baekdu, which is also sometimes spelled Paektu.

As the highest mountain on the Korean peninsula, at about 2,750m above sea level, Mount Baekdu is the mythical origin of the Korean people, featuring in South Korea's national anthem and various North Korean propaganda.

Although Mount Baekdu straddles the North Korea-China border and can be reached from China, where it is known as Changbai Mountain, Mr Moon has never visited.

That is because when he goes up Mount Baekdu, he wants to go "stepping on our soil", Mr Kim Eui-kyeom, spokesman for the presidential Blue House, told reporters on Wednesday.

An active volcano, Mount Baekdu is dotted with secret camps and historical sites from Korea's guerrilla war against the occupying Japanese in the 1940s. A funicular railway takes tourists up the mountain, which also holds a huge crater lake.

"I have a dream that I have not been able to fulfil for a long time, which is trekking Mount Baekdu and the Kaema Plateau (in North Korea)," Mr Moon said during a banquet after his first summit with Mr Kim Jong Un in April, which took place at the Demilitarised Zone separating the two neighbours.

"I believe Chairman Kim will make that dream come true for sure."

North Korea says Mr Kim's grandfather and father were born at Mount Baekdu, a centrepiece of the North's idolisation and propaganda campaign to highlight the ruling family's sacred bloodline.

Mr Kim previously visited the mountain around major developments in North Korea, such as in late 2013 before he executed top officials including his uncle Jang Song Thaek, and after North Korea's fifth nuclear test in 2016, North Korea watchers say.

Mr Moon was born in South Korea in 1953 during the Korean War. His parents had fled from the North during the war, sailing for three days on the deck of a US ship packed with refugees.

A former human rights lawyer, he said in a 2017 book published months before his election as president that he wanted to "finish his life" in his mother's North Korean hometown doing pro-bono service.

"When peaceful reunification comes, the first thing I want to do is to take my 90-year-old mother and go to her hometown," Mr Moon wrote in the book.