The talks, held in the border village of Panmunjom in the demilitarised zone (DMZ), followed on from an inter-Korean summit in April at which leaders of the two Koreas had agreed to defuse tensions and cease "all hostile acts".
On Tuesday, following their historic Singapore meeting, Trump and Kim issued a joint statement that reaffirmed the North's commitment to "work toward complete denuclearization of the Korean Peninsula" and gave U.S. guarantees of security to North Korea.
"The sequence will be different this time", the top United States diplomat told reporters at the joint press conference with his South Korean and Japanese counterparts in Seoul.
North Korea fired at least two missiles over Japan a year ago as it sought to develop a weapon capable of reaching the USA mainland with a nuclear warhead.
Turning to a trilateral sit-down between the top diplomats of South Korea, U.S. and Japan.
He characterized them as 'very expensive, ' however, and portrayed their end as an economic decision rather than a negotiated concession that the US had previously said it wouldn't budge on.
Pompeo is expected in Beijing later on Thursday to update Chinese officials on the Singapore summit.
The Sankei Shimbun said Kim discussed the possibility during historic talks Tuesday with US President Donald Trump.
The two clasped hands for a long while Tuesday as they posed for photos in front of a row of US and North Korean flags.
US Secretary of State Mike Pompeo said China - Pyongyang's sole major ally and main trading partner - has reaffirmed its commitment to United Nations sanctions against North Korea until full denuclearisation of the regime is achieved. "They are fighting hard to downplay the deal with North Korea". Trump had the video made for Kim and personally showed it to him on an iPad when the two met.
Trump had raised eyebrows on Tuesday by describing his own country's drills on the Korean peninsula as "provocative", a term used by the North for the exercises. -South Korean joint air exercise, put off a high-level inter-Korean meeting indefinitely on May 16 - the very day it was scheduled to be held.
But on his way to Singapore, "I saw what took place at this [Justin Trudeau] news conference, and I said, "That's not really what happened".
Pyongyang in return "commits to work toward complete denuclearisation of the Korean peninsula".