North Korea on Thursday warned the South to stop "meddling" in talks between Pyongyang and Washington, repudiating its neighbour days before US President Donald Trump arrives in Seoul amid a nuclear deadlock.
He also said the letters Trump and Kim have recently exchanged show that their "willingness to engage in dialogue has never faded".
South Korean President Moon Jae-in said this week that North Korean and USA officials are holding "behind-the-scenes talks" to arrange a third summit, though he and Kim Yeon-chul offered no details.
The Department of Foreign Affairs and Trade said it was providing consular assistance to the family. North Korean officials frequently denounce him as "reckless", the very same insult deployed by the Foreign Ministry on Wednesday.
"If the United States is to move towards producing a result, time will not be enough".
Moon, a liberal who met Kim three times a year ago, lobbied hard between Washington and Pyongyang to facilitate diplomacy and find a negotiated resolution to the North Korean nuclear issue.
Pompeo was talking to reporters at Joint Base Andrews on Sunday - on his way to the Middle East, Asia, and ultimately the G20 Summit - when he was asked a two-part question about sanctions against Iran and the possibility of talks resuming with North Korea in the near future.
Seoul is set to host the US President this weekend as it tries to rekindle nuclear talks that have stalled since the collapse of a second summit between Trump and Kim in Hanoi in February.
Trump's visit to the South had fuelled media speculation over a possible trilateral summit with Kim and Moon, but Trump himself has said he will not be meeting Kim.
As for the sanctions, so today some 80-plus percent of the North Korean economy is sanctioned.
Chinese President Xi Jinping told Moon that Kim's commitment to denuclearisation remained unchanged, South Korea's presidential Blue House said on Thursday.
Seoul and the United States, for their part, maintain that the sole goal of the Thaad system is to defend against North Korean missiles.
The North Korean leader told his closest partner that he is "willing to promote reconciliation with South Korea, and that he is not seeking to change the trend of dialogue on the Korean Peninsula", Seoul said. Daily Shincho magazine said Wednesday that Fujimoto had been arrested on alleged espionage charges, but a Japanese intelligence official told the NK News service the report was "unconfirmed". Moon also said talks between the two Koreas have been under way through unspecified "various channels".
The announcement follows the fifth meeting between the Chinese and South Korean Presidents held on the sidelines of Friday and Saturday's G-20 summit in Osaka.
Kim Yeon-chul said that while both the Iran and North Korea nuclear issues share some things in common, they should not be viewed in the same way because of what he called joint efforts by Washington and Pyongyang to salvage the stalemated nuclear talks.