The comment from Gen. Oleksandr Syrskyi came a day after the New York Times reported that Moscow had assembled a force of 50,000 troops, including North Korean soldiers, in the region bordering Ukraine for an attack.
"Carrying out an order of their military leadership, (the Russian forces) are trying to dislodge our troops and advance deep into the territory we control," Syrskyi wrote on the Telegram messaging app.
Syrskyi made no reference to the possible presence of North Korean troops among the Russian forces.
Western countries, South Korea and Ukraine have all said that North Korea has sent troops to Russia.
Russia has neither confirmed nor denied the presence of North Korean troops on its territory. However, on Saturday, President Vladimir Putin signed into law a treaty on his country's strategic partnership with Pyongyang, which includes a mutual defense provision.
Ukraine launched its incursion into Kursk in August, seizing settlements in its first such deployment into Russian territory since Moscow launched its February 2022 full-scale invasion.
Russia, however, has continued its slow but steady advance across much of eastern Ukraine, where it is capturing village by village in a bid to seize the entire industrialized Donbas region.
In his statement, Syrskyi said the Kursk operation was still successfully diverting Russian forces from mounting heavier attacks on the eastern front.
"These tens of thousands of enemies from the best Russian shock units would have stormed our positions in the Pokrovsk, Kurakhiv or Toretsk directions, which would have significantly worsened the situation at the front," he said.
The New York Times report, citing a U.S. assessment, said Russia had built up the Kursk force without needing to move troops from eastern Ukraine.