Russian President Vladimir Putin says a Ukrainian sabotage group entered a Russian border region on Thursday and opened fire on civilians in a "terrorist act".
Earlier the governor of Bryansk region said "saboteurs from Ukraine" had fired at a civilian car in Lyubechane, a border village, killing one person and injuring a child.
Kyiv strongly denied the Russian claim.
The alleged incident has not been independently verified.
Mykhaylo Podolyak, an adviser to Ukraine's President Volodymyr Zelensky, tweeted that it was "a classic deliberate provocation". "RF [Russia] wants to scare its people to justify the attack on another country," he said.
Russia has previously reported some Ukrainian missile and drone strikes on Russian border areas, including Bryansk region. But there have been no confirmed reports of Ukrainian ground forces infiltrating Russia.
Mr Putin's spokesman Dmitry Peskov said "steps to destroy these terrorists are being taken". Russia's Federal Security Service (FSB) said FSB forces and regular troops were battling "Ukrainian nationalists" who had crossed into Russia.
Speaking on Russian state TV, President Putin said "today they committed another terrorist act, another crime, penetrated the border area and opened fire on civilians".
"They saw that it was a civilian car, that civilians and children were sitting there, and opened fire. It is exactly such people who set themselves the task of depriving us of historical memory. They will achieve nothing, we will put the squeeze on them," he said.
A video has appeared online claiming to show members of the Ukraine-based Russian Volunteer Corps (RVC) outside a local clinic. One armed man in the video, posted on Telegram, says they crossed into Russia.
The investigative journalism group Bellingcat Monitoring describes the RVC as "a unit officially formed last year made up primarily of anti-Putin, anti-Kremlin Russian far-right figures active in Ukraine".
Commenting on the RVC claim, a Ukrainian military intelligence official, Andriy Yusov, said "these are people who are fighting with arms against the Putin regime and those who support him... Perhaps Russians are beginning to wake up, realise something and take some concrete steps".