A document from the governor of Belgorod claims to show damage to buildings during the incursion
Russian Defense Minister Sergei Shoigu promised a “stern response” to cross-border incursions from Ukraine.
His comments came after Moscow said it defeated an attack in the Belgorod region.
However, regional governor Vyacheslav Gladkov said there had been a “large number” of drone attacks overnight.
Ukraine denies any involvement in the raid – and two Russian paramilitary groups opposed to Russian President Vladimir Putin say they were behind it.
Attackers entered Russian territory from Ukraine on Monday.
Reporting to Defense Ministry officials on the incursion, Mr Shoigu said “more than 70 Ukrainian nationalists” had been killed and the rest had been returned to Ukraine.
“We will continue to respond to such actions by Ukrainian activists quickly and extremely harshly,” he said.
Both Russian paramilitary groups – the Russian Volunteer Corps (RDK) and the Russian Freedom Legion (LSR) denied suffering any casualties and said a Russian motorized rifle company was destroyed.
Claims of losses by belligerents have not been independently verified.
Russia also claims that Western military vehicles were used in the incursion.
He posted photos of destroyed US vehicles apparently at the scene of the fighting, but some Ukrainian military experts and bloggers suggested they might have been staged.
The United States said it was skeptical of the veracity of reports that US-supplied weapons were used in the incursion and did not “encourage or permit insider strikes.” of Russia”.
But Kremlin spokesman Dmitry Peskov said the vehicles were evidence of growing Western military involvement in Ukraine.
“It’s no secret to us that more and more equipment is being delivered to the Ukrainian Armed Forces. It’s no secret that this equipment is being used against our own army,” he said.
“We draw the appropriate conclusions.”
The Russian Defense Ministry released photos of abandoned or damaged Western military vehicles, but some claimed the images were staged
Meanwhile, attacks in the area appear to be continuing.
Mr Gladkov said the night drone attacks were mainly dealt with by air defenses, but damage was caused to cars, private homes and administrative buildings in and around the city of Belgorod, as well as in the border district of Borisovka.
No one was injured in the attacks, he added.
A ‘small fire’ broke out after a gas pipeline was damaged in the Grayvoron district.
Low-intensity attacks in Russian border regions such as Belgorod and Bryansk have become frequent in recent weeks.
Mr Gladkov said farm workers went to the fields with helmets and bulletproof vests due to the threat of attacks.
Villages in Belgorod near the border were evacuated on Monday after coming under fire.
Monday’s raid led Moscow to declare a counter-terrorism operation, giving authorities special powers to suppress communications and popular movements.
The measures were not lifted until the following afternoon, and even then one of the paramilitary groups claimed that it still controlled a small part of Russian territory.