The venue is yet to be decided with speculations that it could be Bangkok or Singapore.
The meeting comes days after N Korean leader warned of 'new path' if US does not ease sanctions.
He also suggested for the first time that the country would no longer produce nuclear weapons.
The two moves send conflicting signals at a time of sensitive negotiations.
However the S Korean president did not elaborate further.
White House looking at scheduling a meet between the two leaders.
'I salute President Trump and the US flag every day to show how much I trust him,' says a 69-year-old Vietnam war veteran.
Trump and Kim Jong Un may have shook hands on the matter, but N Korea's denuclearisation is still a minefield.
However, no second meeting between the two leaders is currently planned.
This is seen as a positive gesture after the June summit between US President Donald Trump and N Korean ruler Kim Jong-un.
N Korean leader expected to brief Chinese president on his summit with US president Donald Trump.
Dennis Ignatius believes this sends a signal to N Korea that its outrageous behaviour will be rewarded.
In a historic summit in S'pore, they hold a comprehensive and sincere exchange of opinions.
The answer may be forthcoming today in S'pore where Kim Jong Un meets Donald Trump.
COMMENT | Whatever agreement is struck, it will likely be wafer-thin.
Officials from both sides are trying to push the denuclearisation agenda forward ahead of Tuesday's summit.
Capitalising on the country's attempt to break out of its isolation could reduce South China Sea tensions, he believes.
Security for Kim in Singapore will be tighter than for any other VIPs, predicts an analyst.
Singapore says it is 'absolutely' in its best interests to contribute to the US-North Korea peace process.
The summit is scheduled to start on the morning of June 12.
Defence Secretary Jim Mattis anticipates 'bumpy road' ahead in talks with Pyongyang.
The surprise meeting is held to get planned talks between Kim and Trump back on track.
Trump faces a difficult task persuading Kim to abandon nuclear weapons.
The North Korean leader also stepped on South Korean soil, the first to do so since the end of the 1950-53 Korean War.
Rogue state says it has fulfilled its objectives, and that there is no need to conduct further tests.
Kim claps along to some of the songs and poses for photos with the performers.
The visit is Kim's first known journey abroad since he assumed power in 2011.
If the summit fails, the cost could be higher than in the past.