Moscow's troops have driven out Ukrainian forces from nearly all of Russia's western Kursk region, Russia's military chief Valery Gerasimov said on Saturday.

"The bulk of the area where the invasion took place has now been cleared," Gerasimov told President Vladimir Putin in a televised meeting.

"It's 1,260 square km, 99.5%."

Russia has been trying to eject Ukrainian forces from Kursk since August last year after Kyiv's troops mounted a surprise incursion that embarrassed Putin and which Ukrainian President Volodymyr Zelenskiy hoped would give him a bargaining chip in any future talks to end the war.

Gerasimov updated Putin on the battlefield developments, which Reuters could not independently verify, shortly before the Kremlin chief announced a unilateral Easter ceasefire in Ukraine.

Gerasimov said Ukraine was holding onto just 3 square km of Kursk around the villages of Oleshnya and Gornal, which lie just on the border.

The Defence Ministry said on Saturday that Russia had recaptured Oleshnya from Ukraine.

In recent weeks Russia has retaken a swath of territory inside Kursk and has begun to push ahead into Ukraine's neighboring Sumy region.

At the same time, Ukraine has also made a fresh push into Russia's Belgorod region, south of Kursk. Gerasimov told Putin that troops were successfully suppressing Ukrainian attacks there.