"In the areas of the Kursk operation, new assaults have taken place," Zelenskiy said during his Friday address.
"Russia has once again deployed North Korean soldiers alongside its troops."
According to Zelenskiy, a "significant number" of enemy troops were destroyed.
He gave no details but said the losses were in the hundreds.
Russia's Ministry of Defence said on Saturday that it had repelled a Ukrainian counterattack in the Kursk region.
Russia said on Friday its forces had captured the mining town of Toretsk in their latest breakthrough in eastern Ukraine's Donetsk region, where Ukrainian defences are creaking.
Ukrainian officials did not confirm the report.
South Korea's military said last month that it suspected North Korea was preparing to send additional troops to Russia after its soldiers suffered heavy casualties.
North Korea has been supplying a vast amount of artillery and other conventional weapons to Russia, and last October it sent about 10,000-12,000 troops as well, according to US, South Korean and Ukrainian intelligence.
Meanwhile, one person was killed and 10 wounded on Saturday in a Ukrainian strike on the city of Makiivka, a town in Ukraine's partially occupied eastern Donetsk region, Moscow-installed officials said.
Russia's Defence Ministry also said that 36 Ukrainian drones were shot down overnight into Saturday in four regions of western and southwestern Russia.
No casualties were reported but Rostov regional Governor Yuri Slyusar said 14 apartment buildings were damaged in the southwestern city of Rostov-on-Don.
Moscow sent 139 drones into Ukraine overnight into Saturday, Ukrainian officials said.
According to Ukraine's air force, 67 drones were destroyed and 71 electronically jammed.
