The victorious end of the battle to liberate Russia's Kursk region showed the "highest strategic level of the firm militant friendship" between North Korea and Russia, KCNA state news agency cited the North's ruling party as saying.
Russia said last week Ukrainian forces had been expelled from the last Russian village they had been holding, although Kyiv denied the claim and said their troops were still operating in Belgorod, another Russian region bordering Ukraine.
Russia's President Vladimir Putin expressed his personal gratitude to North Korea and Kim.
"We will always honour the Korean heroes who gave their lives for Russia, for our common freedom, on an equal basis with their Russian brothers in arms," Putin said in a statement released by the Kremlin.
The Central Military Commission of the North's ruling Workers' Party said leader Kim made the decision to deploy troops under the comprehensive strategic partnership treaty he signed with Putin in 2024.
Under Kim's orders, North Korean military units fought with the same commitment they would have shown if they were fighting for their own country, KCNA cited the Commission as saying.
"They who fought for justice are all heroes and representatives of the honour of the motherland," KCNA quoted Kim as saying.
North Korea "regards it as an honour to have an alliance with such a powerful state as the Russian Federation," KCNA said.
The US State Department demanded North Korea's deployment to Russia and any support by Russia in return must end, adding Russia had violated UN Security Council resolutions by training North Korean soldiers.
Countries such as North Korea, whose support has "perpetuated the Russia-Ukraine war, bear responsibility," a State Department spokesperson told Reuters. 
South Korea said Monday's confirmation of the troop deployment was an "admission of criminal act," and condemned the North for the "inhumane and immoral" decision to send its young people to battle with the intention of propping up its regime.
North Korea sent an estimated total of 14,000 troops, including 3000 reinforcements to replace its losses, Ukrainian officials have said. Lacking armoured vehicles and drone warfare experience, they took heavy casualties but adapted quickly.
Ukraine's Special Operations Forces said on Thursday they had killed a unit of 25 North Korean soldiers in Kursk. They released a video showing one of the slain soldiers and their possessions, which included a note written in Korean.
North Korea has also supplied weapons including artillery munitions and ballistic missiles, South Korean officials have said.
Russia confirmed on Saturday for the first time that North Korean soldiers have been fighting alongside Russians in Kursk.
Neither Russia nor North Korea had previously either confirmed or denied the deployment.
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