It said Kim directed a "tactical guided weapons firing test".
He also noted that the further development and strengthening of friendly Korean-Russian relations is of common interest for the two states. Russian Federation said earlier this week it is preparing for Kim to meet with President Vladimir Putin, setting the stage for consultations between the long-time allies after Kim's nuclear talks with the US broke down.
Trump last week rejected a call for confidence-building joint economic projects between Seoul and Pyongyang, and his national security adviser said Wednesday that the USA would need to see more evidence that Kim was ready to give up nuclear weapons before scheduling a third summit.
The dictatorial regime's request came just hours after North Korea claimed it had just tested a "new-type tactical guided weapon" amid efforts by the United States and Japan to create negotiations for denuclearization, the Associated Press reports. Later in the day, Russian President Vladimir Putin congratulated Kim on his re-election, confirming his commitment to "cooperation on pressing bilateral and regional issues".
The Kremlin gave no further details of the summit between Putin and Kim in the statement on its website, but Moscow has been saying for months that it was working on such a meeting.
In Washington, Acting Defense Secretary Patrick Shanahan confirmed that North Korea conducted a test launch but said it did not involve a ballistic weapon and did not trigger any change in US military operations.
The US government replied by saying it remains "ready to engage North Korea in a constructive negotiation".
This comes after Pyongyang tested a new tactical weapon this week, and called for Pompeo to be removed as President Trump's top negotiator.
It was a response to Pompeo's remarks earlier this week in which he dismissed Kim's warning in a speech on Friday that set an end-of-year deadline for the United States to adopt a mutually acceptable approach to talks or risk reviving tensions.
In testimony to a Senate subcommittee last week, Pompeo, who flew to Pyongyang four times a year ago, was asked if he would agree with the characterisation of Kim as a "tyrant". But he could provide important political cover or economic aid for North Korea - and a potential headache for Trump - if he chooses to play a bigger role.
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South Korea's Unification Ministry, at the time, cautiously said the "ultramodern" weapon was likely to be a conventional one - perhaps a long-range artillery piece like a multiple rocket launcher - that did not appear to be in violation of Pyongyang's self-imposed moratorium on nuclear and missile testing.
Harry Kazianis, the Korean studies director for the USA -based Center for the National Interest, noted that Kim never promised to stop all weapons testing.
North Korean officials accompanying Kim at the test included Ri Pyong Chol and Kim Jong Sik, two senior officials from the North's Munitions Industry Department who have been sanctioned by the US Treasury Department for their activities related to the country's ballistic missile program.
"Even if this is not a "missile" test the way we strictly define it, these people and MID are all sanctioned entities for a reason", Hanham said.
A US State Department spokesperson said Thursday they were "aware of the report" of Kwon's remarks.
South Korea had not detected anything on radar so it was unlikely to have been a missile, a military official told AFP. South Korea's Joint Chiefs of Staff said it is analysing the test but did not specifically say what the weapon appeared to be.
Joseph Yun, who served as USA special representative for the DPRK until past year, said the country had always been dubious about Pompeo, seeing him as a hardline conservative skeptical of engagement with it.
Upping the ante in the diplomatic standoff, North Korea's foreign ministry described Pompeo as "reckless" and immature and said it wanted him replaced.
If the summit takes place, the meeting will mark the first time Putin is meeting with a North Korean leader since Kim assumed power.