It is unclear what cooperation he was referring to. The ambassador did not confirm allegations that North Korea has sent troops to fight with Russia’s military.
Pyongyang has also not commented on the allegations.
South Korea has long accused the North of supplying weapons to Russia for use in the war against Ukraine, but it says the current situation has gone beyond the transfer of military materials.
Some South Korean media reports have suggested as many as12,000 North Korean soldiers are expected to be deployed.
“[This] not only gravely threatens South Korea but the international community,” Kim said on Monday.
Moscow and Pyongyang have stepped up cooperation after their leaders Vladimir Putin and Kim Jong Un signed a security pact in June, will pledges that their countries will help each other in the event of “aggression” against either country.
Last week, Putin introduced a bill to ratify the pact.
Pyongyang’s deployment of troops to fight with Russia “would mark a significant escalation” in the conflict, Nato Secretary-General Mark Rutte said on Monday.
In a phone call with Rutte on Monday, South Korea’s President Yoon Suk Yeol urged the alliance to explore “concrete countermeasures”, adding that he will take steps to strengthen security cooperation between South Korea, Ukraine and Nato.
British Foreign Minister David Lammy, who is visiting Seoul, called Russia’s actions “reckless and illegal”, adding that London would work with Seoul to respond, according to Yoon’s office.
The United States and Japan have also condemned the deepening military ties between North Korea and Russia.
Meanwhile, in response to a BBC question about the alleged North Korea-Russia cooperation, Chinese foreign ministry spokesperson Lin Jian said that China hopes all parties will work to de-escalate the situation and aim for a political solution to the Ukraine crisis.
Some defence experts told BBC Korean that North Korea’s involvement could complicate the war.
“North Korea’s involvement could open the door for greater international participation in the conflict, potentially drawing in more countries,” said Moon Seong-mok from the Korea National Strategy Institute.
“The international community will likely increase sanctions and pressure on both Russia and North Korea, but it remains to be seen whether North Korea’s involvement will truly benefit either country,” Dr Moon said.
But others believe the Russian military units will have difficulties incorporating North Korean troops into their frontlines.
Apart from the language barrier, the North Korean army has no recent combat experiences, they said.
Valeriy Ryabykh, editor of the Ukrainian publication Defence Express, said the North Korean soldiers could be asked to guard sections of the Russian-Ukrainian border, which will free up Russian units to fight elsewhere.
“I would rule out the possibility that these units will immediately appear on the front line,” he said.
Additional reporting by Sangmi Han, Jake Kwon and Hosu Lee in Seoul