Russian President Vladimir Putin said a Ukrainian sabotage group had knowingly fired at civilians on Thursday in what he called a "terrorist act" on Russian territory close to the border.
Russian news agencies reported earlier that a group of Ukrainian saboteurs had taken hostages in the Bryansk region, while the regional governor said two had been killed and a child had been injured.
Ukrainian officials denied responsibility.
In televised remarks, Putin said Russia would prevail in the face of such attacks.
The Kremlin said earlier on Thursday that measures were being taken to destroy the "Ukrainian terrorists" who had mounted a cross-border attack.
Putin receiving regular updates on 'Ukrainian terror attack'
Kremlin spokesman Dmitry Peskov said President Vladimir Putin was receiving regular updates from security agencies and Defence Minister Sergei Shoigu about the situation.
Peskov denied reports that Putin planned to hold an emergency meeting of the Security Council on Thursday, but said he would hold a meeting of the Council on Friday when it convenes regularly.
"They won't achieve anything. We will crush them," said Putin, saying the group was made up of the kind of people who wanted to rob Russia of its history and language.
In two videos circulating online, armed men calling themselves the "Russian Volunteer Corps" said they had crossed the border to fight what they called "the bloody Putinite and Kremlin regime."
Calling themselves Russian "liberators," the armed men called on Russians to take up arms and rise up against the authorities. They said they did not open fire on civilians.
Reuters could not immediately verify the videos' authenticity.
Kremlin spokesman Dmitry Peskov told reporters that law enforcement agencies would determine who was responsible and Putin was being briefed by security chiefs on the situation.
Kyiv's accusations
Ukrainian presidential adviser Mykhailo Podolyak wrote on Twitter: "The story about (a) Ukrainian sabotage group in RF (Russian Federation) is a classic deliberate provocation."
He said Russia "wants to scare its people to justify the attack on another country & the growing poverty after the year of war."
A spokesman for Ukrainian military intelligence suggested the makeup of the sabotage group was a sign of internal strife inside Russia.
"These are people who with weapons in their hands are fighting the Putin regime and those who support it... Maybe Russians will begin to wake up, realize something and take some concrete steps," Andriy Yusov told Ukrainian outlet Hromadske.
Russia's FSB security service said in a statement to Russian news agencies on Thursday that its own forces and the army were trying to liquidate what it described as "an armed group of Ukrainian nationalists" who had crossed the border.
Bryansk Governor Bogomaz said on his Telegram channel: "Today, a Ukrainian sabotage and reconnaissance group penetrated the Klimovsky district in the village of Lubechanye. "Saboteurs fired on a moving car. As a result of the attack, one resident was killed and a ten-year-old child was wounded."
He said Ukrainian armed forces had carried out a drone attack and fired artillery at other areas near the border.
Reuters was unable to immediately verify the reports.
British military intelligence said on Wednesday that Russia was launching drone attacks on Ukraine from the Bryansk region, which lies to the north of Ukraine and is closer to its capital Kyiv than other launch sites.
The Russian state news agency TASS said the Ukrainians had infiltrated two villages, taking local residents hostage in one of them. The RIA news agency said several people had been taken hostage in a store in the village of Lubechanye, less than one kilometer from the border with Ukraine.
Russia has accused Ukrainian saboteurs of infiltrating Bryansk before.
In December, the FSB said a four-person Ukrainian "sabotage group" had been "liquidated" while trying to enter Bryansk.
Putin told the FSB this week that it needed to step up its guard against espionage and what he called terrorist threats emanating from Ukraine and the West.
"Your task is to put a barrier in the way of sabotage groups, to stop attempts to illegally transport weapons and ammunition into Russia," he said in a speech on Tuesday.