Eyre spoke as U.S. Secretary of State Mike Pompeo headed for his fourth visit this year to North Korea, seeking to break an impasse in denuclearization talks and clear the way for a second summit between Kim and U.S. President Donald Trump.
Pompeo and Kim met for about two hours and then had lunch together. "I look forward to seeing Chairman Kim again, in the near future", Trump wrote on Twitter on Sunday. The Secretary of State then put his hand on Kim's shoulder and the pair smiled.
"I am really pleased for this opportunity".
He also was supposed to meet with Kim in August, but Trump canceled the trip at the last minute.
Pompeo held talks with North Korean leader Kim Jong Un during the day, and flew into Seoul in the evening.
Pompeo thanked him for hosting the event and conveyed President Trump's regards. Both men spoke through translators.
But the official - part of Mr Pompeo's delegation - did say the trip had been "better than the last time".
The last trip to North Korea for the secretary of state, in July, did not go so well.
North Korea's leader Kim also struck a positive tone during his meeting with Pompeo. On that occasion, he did not meet Kim.
But the official added: 'It's going to a long haul, ' according to The New York Times.
Pyongyang and Washington have clashed over the sequence of denuclearization measures and corresponding compensation - a repeat of past nuclear negotiations between the two countries.
North and South Korea leaders met last month to rekindle the peace process.
Kim pledged to work toward denuclearization during the Singapore summit, but Pyongyang's actions have since fallen short of USA demands for irreversible steps to give up its arsenal.
After Pompeo's stop in South Korea, he will visit China before heading home.
The North has accused Washington of making "unilateral and gangster-like" demands on denuclearization and has insisted that sanctions should be lifted before any progress in nuclear talks.
During their meeting on Sunday, Pompeo and Kim also agreed to form a working group "at an early date" to discuss the denuclearisation process and the second summit, according to Moon's press secretary Yoon Young-chan.
Winning the Nobel peace prize is a significant victory for all women suffering from sexual violence in conflicts, Yazidi campaigner Nadia Murad said on Friday in her first remarks after jointly winning the award.
Abe did not speak of differences but highlighted the importance of demonstrating to the world that the U.S. -Japan alliance is "more robust than ever" and stressing the importance of "thorough co-ordination" with Washington on all aspects of North Korea policy. When you factor in the brewing U.S.
Al Jazeera's Rob McBride, reporting from the South Korean capital, Seoul, said Pompeo's meeting with Kim has "been taken as a positive sign that dialogue is still on track".
While in Pyongyang, Pompeo was expected to lay the groundwork for a second summit between Kim and the US President.
After meeting with Kim for more than three hours with Kim in Seoul, Pompeo traveled to Pyongyang to brief National Security Adviser John Bolton and White House Chief of Staff John Kelly on his trip.