KRAMATORSK, Ukraine — Fighting raged for a second day on Tuesday in the Belgorod region of southern Russia as a Ukrainian-aligned paramilitary group claimed to seize villages and rebuff counterattacks, in the most dramatic instance to date of bringing the war into Russian territory.
The Free Russia Legion, a group of Russian volunteers who have taken up arms to fight for Ukraine, claimed responsibility for the incursion, while Kyiv publicly denied direct involvement, turning the tables on a Russian strategy that preceded the invasion last year of sending unacknowledged weaponry and soldiers into Ukraine.
Russia’s Ministry of Defense said on Tuesday afternoon that it had pushed the militants back across the border, adding that scores of “saboteurs” had been killed. That claim could not be verified, and people who said they represented the fighters maintained the attacks were continuing and had gained new ground. Those statements also could not be verified.
The incursion could compel Russia to divert soldiers from a long and unevenly defended front in southeastern Ukraine ahead of a long-anticipated Ukrainian counteroffensive, military analysts said. It seemed intended as well to unnerve and embarrass the Russian leadership by showing a weakness in border defenses.
Against a bucolic background of green farm fields, smoke billowed from explosions during the fighting, according to drone video verified as authentic by The New York Times.
Representatives of the Free Russia Legion said on Tuesday that Ukrainian officers were aware of the operation but had not directed it. The tanks deployed in the attack against Russia, they said, had been captured from Russia’s army in Ukraine. Russia claimed it had captured an American-made armored vehicle designed to withstand land mines that had been used in the attack.
The Kremlin spokesman, Dmitri S. Peskov, said that even if the attackers were ethnic Russians, they are “Ukrainian militants” whose violence justifies Moscow’s broader war against its neighbor.
“This once again confirms that Ukrainian militants are continuing their activities against our country,” Mr. Peskov told reporters on Tuesday.
A deputy Ukrainian defense minister, Hanna Maliar, described the attackers as “Russian patriots” who “rebelled against the Putin” government.
“These are internal Russian trends dictated by the desire of citizens to change the political system of the country and end the bloody war that the Kremlin has unleashed,” Ms. Maliar said Tuesday on Ukrainian television.
The governor of Belgorod region, Vyacheslav Gladkov, said the region had been struck 15 times with artillery on Tuesday morning. He later said one civilian had been killed.
Soldiers and armored vehicles, including some bearing Ukrainian markings, were seen in videos posted online from Belgorod on Monday.
In another Russian border region to the north, Bryansk, a military factory warehouse caught fire on Tuesday near the town of Dyatkovo, local news media reported. Details were not immediately available.
The Free Russia Legion operates under the umbrella of Ukraine’s International Legion, a fighting force overseen by Ukrainian officers.
Ukrainian commanders in the International Legion knew about the operation but had not directed it, Ilya Ponomarev, an exiled Russian politician who described himself as the political representative of the Free Russia Legion, said in a telephone interview on Tuesday.
Mr. Ponomarev maintained the Free Russia Legion’s soldiers had captured about a dozen Russian border guards and were “inside Russia, digging trenches and preparing to defend the land that they liberated.” His claims could not be independently verified.
Mr. Ponomarev described the incursion as an effort to “liberate a certain part of Russian land,” to force the Russian military to divert troops fighting in Ukraine and to destabilize President Vladimir V. Putin’s government.
“We think now they need to reconsider and deploy more forces all along the Ukrainian border,” Mr. Ponomarev said.
A spokesman for the political wing of the Free Russia Legion, Aleksey Baranovsky, said the group captured two villages on Tuesday and held in total about eight square miles of Russian territory.
A senior Ukrainian official, who spoke on the condition of anonymity to discuss the sensitive mission, said that the Free Russia Legion had suffered losses but not enough to affect the fighters’ combat readiness.