The test was announced after satellite images from last week were released showing activity at North Korea's main nuclear site.
In a sign that the North is leaving its options open, Russian Federation also confirmed Wednesday that preparations are underway for a possible summit between Kim and President Vladimir Putin. It was not clear whether it was the same weapon tested this week.
"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 Jong Gun, director general of the ministry's Department of American Affairs said, according to the official KCNA news agency.
According to Cha, recent developments in North Korea and Seoul-Washington relations do not bode well for President Moon Jae-in's hopes to mediate between Pyongyang and Washington.
The stabilized relationship between the United States and North Korea has always been an accomplishment touted by President Donald Trump, who cited the lack of missile tests as an example of his diplomatic success.
U.S. special envoy for North Korea Stephen Biegun was also in Moscow, the State Department said.
It was the North's first weapon test since the February talks between Kim and U.S. President Donald Trump in Vietnam.
"Our scientists, technicians and workers are, indeed, great and there is no weapon impossible to make when they are determined to do", Kim said, KCNA reported.
US Special Representative for North Korea Stephen Biegun was in Moscow on Wednesday and Thursday to meet Russian officials to discuss ways to advance a "final, fully verified denuclearisation of North Korea", the US said. "It was air force inspection yesterday and short-range missile test today, so we can even go on to guess there may be a nuclear provocation next year".
During a speech at Texas A&M on Monday, Pompeo said Kim promised to denuclearize during his first summit with Trump and that USA officials were working with the North Koreans to "chart a path forward so we can get there".
DPRK leader Kim Jong Un supervised the test.
And in an apparently coordinated response by his administration, both the Pentagon and State Department issued the same curt statement when asked for comment by The Japan Times: "We are aware of the report, and have no further comment".
Pompeo is "talking nonsense" by trying to finish working-level negotiations between North Korea and the United States by the end of the year, "which subjects him to public ridicule", the statement said.
KCNA said Kim oversaw the testing of the weapon Wednesday, explaining that it was tested "in various modes of firing at different targets", had a "peculiar mode of guiding flight", and could carry a powerful warhead.
The U.S. and South Korean governments have so far not commented on the test.
Washington says it won't allow the North's desired sanctions relief until the nation commits to verifiably relinquishing his nuclear facilities, weapons and missiles.
Putin has previously expressed positions sympathetic to Kim's regime, saying previous year that Pyongyang must be given guarantees in exchange for de-nuclearisation.