Ukrainian official remained quiet about the scope of the operation.
Putin told cabinet officials he would meet top defence and security officials to discuss what he called the "indiscriminate shelling of civilian buildings, residential houses, ambulances with different types of weapons".
He instructed the cabinet on Wednesday to co-ordinate assistance to the Kursk region.
The head of the region urged residents to donate blood due to the intense fighting.
Kursk's governor said hundreds of people had been moved from the areas under shelling. (AP PHOTO)
"In the last 24 hours, our region has been heroically resisting attacks" by Ukrainian fighters, acting Governor Alexei Smirnov said on Telegram, adding that all emergency services were on high alert.
Smirnov also said authorities had moved more than 200 people from areas under shelling, while several thousand others left in their own vehicles.
If confirmed, the reported battalion-sized cross-border foray would be among Ukraine's largest since Russia's full-scale invasion, and unprecedented for its deployment of Ukrainian military units.
Kyiv's aim could be to draw Russian reserves to the area, potentially weakening Moscow's offensive operations in several parts of Ukraine's eastern Donetsk region where Russian forces have increased attacks and are advancing gradually toward operationally significant gains.
But it could risk stretching outmanned Ukrainian troops further along the front line, which is more than 1000km long.
Even if Russia were to commit reserves to stabilise the new front, given its vast manpower and the relatively small number of Ukrainian forces engaged in the operation, it would likely have little long-term impact.
However, the operation could boost Ukrainian morale at a time when Kyiv's forces are facing relentless Russian attacks and are expected to face more challenges in coming weeks.
Several Ukrainian brigades stationed along the border region said they could not comment.
Ukraine's defence ministry and general staff also would not comment.
Russian forces have swiftly repelled previous cross-border incursions but not before they caused damage and embarrassed authorities.
The Russian defence ministry said on Tuesday that up to 300 Ukrainian troops, supported by 11 tanks and more than 20 armoured combat vehicles, had crossed into Russia and suffered heavy losses.
Russia has swiftly repelled previous Ukrainian incursions but not before they caused damage. (file) (AP PHOTO)
It said on Wednesday that military and border guard troops "continued to destroy Ukrainian military units in the areas alongside the border in the Kursk region".
The ministry said Russian forces backed by artillery and warplanes "didn't allow the enemy to advance deeper into the territory of the Russian Federation".
It was not possible to verify the Russian claims.
Open-source monitors have also not been able to verify the claims.
Responsibility for previous incursions into Russia's Belgorod and Bryansk regions has been claimed by two murky groups: the Russian Volunteer Corps and the Freedom of Russia Legion, which are made up of Russian citizens and have fought alongside Ukrainian forces.
Disinformation and propaganda have played a central role in the war, now in its third year.
Some Russian war bloggers who have proved knowledgeable about the war said Ukrainian soldiers were in Kursk.
Rybar, a Telegram channel run by Mikhail Zvinchuk, a retired Russian defence ministry media officer, said Ukrainian troops had seized three settlements in the region and continued to fight their way deeper into it.
Another pro-Kremlin military blog, Two Majors, claimed that Ukrainian troops had advanced up to 15km into the region.
Neither claim could be independently verified.
The Kursk region's border with Ukraine is 245km long, making it possible for saboteur groups to launch swift incursions and capture some ground before Russia deploys reinforcements.
