The Kremlin's response to Ukrainian soldiers controlling a slice of Russia's Kursk region has been muted so far as it gets on with business as usual rather than making threatening speeches.

President Vladimir Putin has opted for his go-to style of downplaying uncomfortable news, referring to the largest incursion in Russia since World War II as "the situation that has developed."

"It's the usual way he acts in similar circumstances: disappearing until the situation sizzles down and then making it look like everything is normal," said political scientist Ekaterina Schulmann.