But progress has been scant since then.
The Trump administration has pressed North Korea to give up its nuclear weapons program, which threatens the US, before it can expect any concessions.
North Korea wants an easing of punishing US-led sanctions, security guarantees and a formal end of the 1950-1953 Korean War, which ended in a truce, not a treaty.
Kim left the North Korean capital of Pyongyang about 5pm on Saturday local time in an armoured train, Russia’s TASS news agency said, citing a North Korean diplomatic source.
Two witnesses in the Chinese border city of Dandong, where the main rail line from North Korea arrives in China, said a train had crossed the Yalu River into China around 9.30pm.
South Korea’s Yonhap news agency and broadcaster YTN also reported that a train suspected to be carrying Kim had arrived in Dandong.
Chinese security chased away people trying to take photographs, one witness said.
It was unclear if Kim was on the train. China has declined to answer questions about Kim’s travel plans via the country.
It could take Kim at least two and a half days to travel the thousands of kilometres through China by train to Vietnam.
A senior security official in Vietnam told Reuters that Hanoi had been expecting a Vietnam-bound train to depart Pyongyang on Saturday, but did not know if Kim himself was on board.
Two sources with direct knowledge of security and logistics planning told Reuters on Wednesday that Vietnam was preparing for Kim to arrive by train.
His train was expected to stop at the Vietnamese border station of Dong Dang, where he will disembark and be driven 170km to Hanoi by car, the sources said.
Vietnamese police have stepped up security around the border station.
On February 26, Vietnam will ban traffic on the road Kim is expected to take to Hanoi from a station on the Chinese border, state media said.