"I am afraid that, if Pompeo engages in the talks again, the table will be lousy once again and the talks will become entangled", Kwon said.
North Korea's call to exclude Pompeo comes a week after the secretary of state agreed Kim is a "tyrant" before a U.S. Senate subcommittee.
The country also said it test-fired a new "tactical guided weapon".
-North Korea summit in February, The Associated Press reported.
The release came amidst an apparent stalemate of diplomatic discussions and an apparent retesting of missile technology by the North Koreans. Previously, Kim oversaw a test of a "tactical weapon" in November, which could allegedly protect North Korea as a "steel wall".
Some in Seoul worry that the North will turn back to actions seen as provocative by outsiders as a way to force Washington to drop its hard-line negotiating stance and grant the North's demand for a removal of crushing global sanctions.
What did North Korea test? President Trump has continued to emphasize the importance of his personal relationship with Kim.
Russian media have been abuzz in recent days with rumours about the first one-to-one meeting between the leaders.
Putin has long expressed his readiness to meet with Kim.
Trump said last month that he "would be very disappointed if I saw testing".
Kim's visit to the testing site came after he visited the North Korean Air and Anti-aircraft Force on Tuesday, according to KCNA.More news: Attorney Michael Avenatti Indicted on 36 Counts of Embezzlement, Fraud, Tax Evasion
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Last year, Kim had said North Korea will stop nuclear tests and launches of intercontinental ballistic missiles, because Pyongyang's nuclear capabilities had been "verified".
But it claimed the weapon has a "peculiar mode of guiding flight" as well as "a powerful warhead".
Melissa Hanham, a non-proliferation expert and director of the Datayo Project at the One Earth Future Foundation, said the North Korean weapon could be anything from an anti-tank weapon to a cruise missile.
The report added that Kim had set goals for "keeping munitions production going, and putting national defense science and technology on [a] cutting edge level". "It shows that North Korea is going on, business as usual, after the failed Hanoi summit".
Even though North Korea's latest test is not likely a ballistic missile, it is still meant to send a message to Trump, said Vipin Narang, a nuclear expert and professor at the Massachusetts Institute of Technology.
"Firing ballistic missile may provide reason for additional sanctions from the worldwide community so North Korea chose to voice their opinion without receiving negative response on their military actions", Moon Sung-muk, an arms-control expert at Korea Research Institute for Strategy, told ABC News. The Pyongyang-based Munitions Industry Department is sanctioned both by the United States and the U.N. Security Council.
"South Korea is likely to have brought up sanctions (in the summit) but the United States has said that it is too early to ease sanctions".
The United States was aware of the North Korean foreign ministry's demand regarding Pompeo, the spokesperson added, but did not provide any further comment.
South Korea's presidential Blue House declined to comment on the test, referring questions to the defence ministry. "The only thing the USA has taken onboard is that a flexible approach may be possible; that a big deal may not be the only option", Cha said.
"However, the US did not detect a missile launch either time so it must be a short-range system, perhaps an artillery system such as a multiple rocket launcher or an antitank guided missile", Klingner told WaPo.