The Russian defence ministry confirmed that airbases in the country's five regions were attacked in a post on social media later on Sunday.
It claimed that "all attacks were repelled" on military airbases in the Ivanovo, Ryazan and Amur regions. The latter base was not mentioned by the SBU sources.
In the Murmansk and Irkutsk regions, "several aircraft caught fire" after drones were launched from nearby areas, the ministry said.
It said all the blazes were extinguished and there were no casualties. "Some of the participants in the terrorist attacks have been detained," it added.
Meanwhile, the Ukrainian authorities say 472 drones and seven ballistic and cruise missiles were involved in a wave of attacks on Ukraine last night.
This would appear to be one of the largest single Russian drone attacks so far. Ukraine says it "neutralised" 385 aerial targets.
In a separate development, Ukraine's land forces said 12 of its military personnel were killed and more than 60 injured in a Russian missile strike on a training centre.
Ukraine's head of land forces, Maj Gen Mykhailo Drapatyi, tendered his resignation shortly afterwards.
He said his decision was "dictated by my personal sense of responsibility for the tragedy".