An unnamed senior Ukrainian intelligence official later confirmed the report to the Financial Times but declined to provide further details.
Ukrainian troops have held large areas of Kursk since early August, after Kyiv launched a surprise cross-border offensive in the region.
Last week, US Secretary of State Antony Blinken said that 8,000 North Korean troops had been moved to Kursk, and he predicted that they would enter the fighting shortly.
"We've not yet seen these troops deploy into combat against Ukrainian forces, but we would expect that to happen in the coming days," he said.
At the same briefing, US Defense Secretary Lloyd Austin said that if North Korean troops took part in fighting or provided combat support they would become "legitimate military targets."
Kovalenko's statement on Monday was the first to suggest that North Korean troops were now actively fighting alongside Russian troops and against Ukraine.
US Air Force Maj. Gen. Pat Ryder said at a Pentagon briefing on Monday that the US was "looking into" the reports.
Last month, South Korean intelligence said that 1,500 North Korean troops had been shipped to Russia for training and likely deployment in the war.
This came after deepening ties between Moscow and Pyongyang following the full-scale invasion of Ukraine in February 2022.
North Korea experts say the partnership between Moscow and Pyongyang is mutually beneficial: While Russia gets much-needed troops, Kim Jong Un is likely gaining an economic boost for his country as well as military know-how from its dealings with Russia.
Representatives from the Armed Forces of Ukraine and Defence Intelligence of Ukraine did not respond to a Business Insider request for comment.