Mr. Gladkov, the Russian governor, initially played down reports of violence, saying there was a “massive information attack” underway, and sought to calm the nerves of residents of a video posted on Monday morning. But in the evening, he said he was putting the region on a counterterrorism footing, giving authorities broad powers to establish temporary restrictions on movement, increase identity verifications and control those telephone communication.
The Kremlin has sought to downplay the incident, with its spokesman Dmitri S. Peskov telling the Tass news agency that it was a Ukrainian attempt to “divert attention from the situation” in Bakhmut, the eastern city it claims of Russian forces at the end of the week captured. after almost a year of war.
While there have been numerous reports of Ukrainians attacking targets across the border over the course of the 15-month conflict, attacks on the ground have been rare. In early March, the Russian Volunteer Corps claimed it had made a brief incursion into the villages of Bryansk, another Russian region on the border with Ukraine.
The Russian Volunteer Corps is led by a Russian nationalist in exile, and is part of a motley collection of groups of Russian citizens who have defied the rule of President Vladimir V. Putin and taken up arms for the Ukrainian cause.
Russia suffered several significant psychological blows during the war, including the explosion that damaged the bridge connecting the occupied Crimea peninsula to the Russian mainland and the sinking of the cruiser Moskva, the flagship of the Black Sea fleet. But Andriy Zagorodnyuk, a former Ukrainian defense minister who now advises his government, said this border incursion was significant because it involved armed troops, which would force Russia to send more of its forces. along the border instead of the front lines.
It could also destroy Russian unity, he said.
“Russians will see that they have problems between their own citizens, so the idea of a united Russia is seriously damaged,” Mr. Zagorodnyuk said.
Oleksandr Chubko, Oleg Matsnev Milana Mazaeva and Riley Mellen contributed to the report.