Russian air defences intercepted Ukrainian drones over two military airfields in Russia, hundreds of kilometres from the border between the two countries, Russia said on Monday.
Falling debris from the unmanned vehicles lightly damaged two aircraft, a defence ministry statement said.
Three Russian servicemen were killed and four injured in the incidents in the Ryazan and Saratov regions.
Long-range strategic bombers are believed to be based at the airfields.
Earlier, large explosions were reported at the Engels airbase in Saratov and the Dyagilevo airbase in Ryazan, but there had been no official comment on their cause.
Hours later, Russia launched a wave of missiles at targets around Ukraine, although Kyiv says it shot most of them down.
Ukraine has not officially commented on the explosions. However, its air force tweeted “what happened?” together with a partying face emoji and images of what looked like a badly damaged aircraft.
Moscow has accused Ukraine of attacking its territory before, but these alleged attacks are deeper into Russia than previous ones. Ukrainian strikes this far into Russia will embarrass the Kremlin, says the BBC’s Russia editor, Steve Rosenberg.
Satellite images taken from Sunday appeared to show a large fleet of Russian heavy bombers at the Engels airbase.
They show what appeared to be type Tu-160 and Tu-95 strategic bombers, which are capable of firing cruise missiles – one of the weapons used in strikes on Ukraine.
Other satellite images released last week appeared to show increased military aircraft activity at the same airbase.
Russian President Vladimir Putin has been informed of the two reported incidents, Kremlin spokesman Dmitry Peskov said.