One woman died and 12 other people were injured in an attack by Ukraine on Russia's Belgorod region, according to its Governor Vyacheslav Gladkov on Tuesday.

In a Telegram statement, Gladkov said another woman is in intensive care in difficult condition after being injured in an attack by Ukrainian "saboteurs" who launched their offensive the day before.

The Russian military and law enforcement continue fighting on the territory of the Grayvoronsky district of the Belgorod region with a "sabotage group" of Ukraine's armed forces, he added.

Gladkov also said residents of nine settlements were relocated due to the infiltration of the group.

The Belgorod region authorities declared a regime of a counter-terrorism operation, which establishes special measures and temporary restrictions, including identity checks.

Commenting on the incident at a press briefing in Moscow, Kremlin spokesman Dmitry Peskov expressed "deep concern," adding that "all necessary measures are being taken" to prevent such events in the future.

Peskov said Russian President Vladimir Putin does not plan to summon an extraordinary meeting of the Security Council over the incident, but a regular meeting may take place at the end of the week.

"Now our special services are finding out the identity, the number (of Ukrainian troops engaged in the attack), and so on," the spokesman said.

Peskov also said he does not expect that deliveries of F-16 fighter jets to Ukraine will change the situation on the battlefield.

"Apparently, the spiral continues to provide (Ukraine) with various more advanced weapons systems and types of weapons. Apparently, it was decided to add planes. But, like all other types of weapons, this is not capable of radically changing the situation at the front," he stressed.

Separately, Ukraine's Sumy region military administration claimed that people are evacuated from the Akhtyr district bordering Russia's Belgorod region.

Ukrainian media, citing Ukraine's military intelligence sources, said on Monday that two groups fighting on the side of the country's armed forces that were formed in March 2022 by ethnic Russians opposing the war -- the Liberty of Russia Legion and the Russian Volunteer Corps -- are behind the attack.

A Ukrainian military intelligence official confirmed that his government was aware of the operation but did not declare its direct involvement.

The groups are also claimed to be behind the March 2 attack on Russia's Bryansk region, which left one person killed and a 10-year-old boy injured.

Russian President Vladimir Putin called the incident in the Bryansk region "a terrorist attack."