Russia says it has spent a third day fighting a surprise Ukrainian offensive in the border region of Kursk, which reports suggest may be among the largest such cross-border incursions undertaken by Kyiv during the war.

A Russian Defence Ministry statement said the Russian military and border guards have blocked Ukrainian forces from pushing deeper into the region in southwestern Russia. It added that the army is attacking Ukrainian fighters trying to advance into the area from Ukraine's Sumy region.

"Attempts by individual units to break through deep into the territory in the Kursk direction are being suppressed," the ministry said.

Heavy fighting was reported near the town of Sudzha, where Russian natural gas flows into Ukraine, raising concerns about a possible sudden stop to transit flows to Europe.

Oleksiy Goncharkeno, a Ukrainian lawmaker, said in a series of posts on Facebook and Telegram that Ukrainian forces had taken control of the gas hub in Sudzha.

"Our men have heroically captured Putin's number one gas valve in Sudzha," Goncharenko said.

However, Kyiv has not officially commented on the apparent incursion in Kursk.

In a video address to the nation late Thursday, Ukrainian President Volodymyr Zelenskyy did not mention the fighting in the Kursk region but emphasized that "Russia brought the war to our land, and it should feel what it has done."

"Ukrainians know how to achieve their goals," Zelenskyy said, adding that he received three "productive reports, exactly the kind our country needs now" on Thursday from the commander of Ukraine's armed forces, Oleksandr Syrskyi.

Ukraine has made gains: Military bloggers

Russia says its military has stemmed Ukrainian advances in the border area about 500 kilometres southwest of Moscow, but military bloggers and open source data indicate Ukrainian troops have made gains in several areas in Kursk.

The Kursk region's acting governor, Alexei Smirnov, briefed Russian President Vladimir Putin on conditions there by video link Thursday. Smirnov said the region plans to equip gas stations with electronic warfare units and to provide them with unspecified armoured defence.

WATCH | Parsing reports out of Russia's Kursk region:

Moscow accuses Ukraine of incursion in Kursk region

Russia claims to be fighting Ukrainian forces following cross-border raids in the Kursk region near a major natural gas transmission hub, though Kyiv has stayed silent on the reported events.

William Taylor, a former U.S. ambassador to Ukraine, saw several reasons why Kyiv might want to undertake a military action of the kind that Russia says is occurring in Kursk.

"They want ... to show that the Ukrainians can indeed push the Russians back," he told CBC's Power & Politics on Thursday.

"It's not just the one time that they did that at the beginning of the war. No, they can still do it."

Taylor said that Kyiv could also be looking ahead to the possibility of eventual negotiations with Russia, "and if the Ukrainians hold some territory, that gives them some leverage."

Russia launched its all-out war against its neighbour in February 2022.

The conflict has cost tens of thousands of Ukrainian civilians their lives and destroyed key infrastructure in the country, as well as buildings and structures in villages and cities alike.