Moon Jae-in, the South Korean president, stepped into the shallow waters of Heaven Lake, regarded as the spiritual home of the Korean people, bent down and scooped up a glassful of water.

Kim Jong-un, his North Korean counterpart, watched from a distance. Moon was fulfilling a long-held dream to visit Mount Paektu, which straddles the border between North Korea and China. At the summit the two men held hands and thrust them into the air as they posed for a photo with their wives, the lake in the background.

The highly symbolic trip capped a three-day visit by Moon to North Korea, the first by a South Korean leader in 11 years. After two days of talks, Kim pledged to close a missile testing site that was crucial to North Korea’s development of intercontinental ballistic missiles, and offered to shut the country’s only known nuclear complex in exchanged for unspecified “reciprocal measures” from the US.

Observers said these measure fell short of expectations in Washington. But inter-Korean relations continue to grow closer, and the trip to Paektu highlighted the close relationship between the two leaders.

Kim hopes to restart negotiations with the US, and hopes to have a second summit with Donald Trump as soon as possible, Moon told reporters when he returned to Seoul. Kim also invited secretary of state Mike Pompeo to Pyonyang, Moon said.

“Chairman Kim expressed his wish to finish complete denuclearization at an early date and focus on economic development,” Moon said, adding that details would have to be worked out between North Koreans and the US.

But US officials have made little progress with the most basic of discussions, such as having North Korea provide an inventory of its nuclear which would become the basis for future talks. Moon said North Korea is ready to accelerate the denuclearisation process, but only if the US makes reciprocal measures, which have not been defined.

If negotiations between Washington and Pyongyang continue to hit roadblocks, it could jeoprdise inter-Korean exchanges since sanctions will likely remain in place. It did not stop Kim from trying to win over the South Korean president, sending him two tons of pine mushrooms, a delicacy.

Moon is an avid hiker and during his first meeting with Kim, in April, he had expressed his desire to visit the mountain, the highest on the Korean peninsula at 2,500 metres (9,000ft).

“I have a dream that I have not been able to fulfil for a long time, which is trekking Mount Paektu,” Moon said at the time. “I believe Chairman Kim will make that dream come true for sure.”

Kim Jong-un and Moon Jae-in with their respective wives at the summit of Mount Paektu. Photograph: Getty Images

The trip to the summit on a sunny morning was less of a trek than a photo op. Both Kim and Moon wore black overcoats and black leather dress shoes, and they travelled to the top by cable car. Outings like this have helped build trust between the two men, something Kim still lacks in his relationship with Trump.

The mountain is featured heavily in North Korean propaganda, and Kim has made trips to its summit after nuclear tests or major announcements, most recently when he declared the country’s nuclear arsenal complete. North Korea’s two previous leaders, Kim’s grandfather and father, are said to have been born in its shadow. This has been used to bolster the Kim family’s claim to a sacred bloodline, though the account has been disputed by some.

Paektu is also a significant symbol in the South, where it is mentioned in the country’s national anthem. Although Moon could have visited the summit sooner from the Chinese side, he had wanted to go by “stepping on our soil”, Kim Eui-kyeom, a South Korean presidential spokesman, said at a briefing.

Moon was scheduled to fly back to Seoul on Thursday afternoon and he will meet Trump in New York next week during the UN general assembly, and Moon said he has a private message from Kim to deliver. The US has invited North Korea’s foreign minister to meet the secretary of state next week in an attempt to restart talks between Washington and Pyongyang.