After the two leaders pledged new steps aimed at salvaging nuclear talks on Wednesday, Moon and Kim decided to use the final day of their three-day summit to go up the symbolic mountain on the Chinese border together.

Moon is known for his love of mountain climbing and has trekked in the Himalayas at least twice.

The president has long stated that visiting Mount Paektu, which can also be spelled Baekdu in the South and is known as Changbai in China, was a "long unfulfilled dream".

"Many people in the South would go to Mount Paektu from the China side, but I decided not to, pledging myself that I would go stepping on our soil," Moon told Kim after reaching the peak of the mountain.

"But time flew so fast, and I thought my wish may not come true, but it did today."

As Moon arrived at an airport near the mountain, some 1000 North Koreans greeted him, waving flowers and chanting "Motherland! Unification!"

Moon and Kim took a cable car together to Heaven Lake, a caldera at the top of the mountain, and walked around the area with their wives and officials from both sides.

Pictures showed Moon and Kim smiling and posing with their wives, and Moon filling a bottle with water from the lake.

"The Chinese envy us because they can't go down to the lake from their side but we can," Kim said.

"We should write another chapter of history between the North and the South by reflecting our new history on this Heaven Lake."

Some senior South Korean officials accompanying Moon suggested inviting Kim and his wife to Mount Halla, the highest mountain and a scenic tourist resort in the South.

"There is our old saying that we greet the sun at Paektu, and greet the unification at Halla," Kim's wife, Ri Sol Ju, said.

Kim said on Wednesday he will visit Seoul in the near future, in what would be the first trip to the southern capital by a North Korean leader.

As the highest peak on the Korean peninsula at about 2750 metres, Mount Paektu is the mythical origin of the Korean people, featured in South Korea's national anthem.

An active volcano, the mountain is dotted with secret camps and historical sites from Korea's guerrilla war against the occupying Japanese in the 1930s and 1940s, in which Kim's grandfather, Kim Il Sung, played a leading role.

Mount Paektu is a centrepiece of the North's idolisation and propaganda campaign to highlight the sacred bloodline of the ruling Kim family.

Australian Associated Press