Multiple air attacks on the Russian border region of Belgorod adjoining Ukraine on Saturday killed two people and injured at least seven, the governor said.
Further east, an overnight drone attack on the Samara region caused a fire at a major oil refinery, the latest in a series of strikes against Russia's fuel industry.
Belgorod governor Vyacheslav Gladkov wrote on Telegram that two districts in his region as well as the regional capital, also called Belgorod, had been hit in drone and air attacks.
"It's shaping up to be a difficult morning," Gladkov said.
"As a result of an air attack by Ukrainian armed forces on Belgorod, three balconies collapsed in an apartment building. One of these apartments was occupied by a married couple. To much grief, the man died from his injuries on the spot," he said.
He posted a photo of a residential building with the facade partially destroyed.
Another person was killed in a drone attack on districts outside the city, he said.
In the Samara region - 1,000 kilometres (620 miles) away from the front lines in eastern -- the local governor reported "several drone attacks" on local oil refineries.
One of them caused a fire at the Kuibyshev refinery, governor Dmitry Azarov said in a statement on Telegram, noting that there were no casualties.
The refinery, run by Russian oil giant Rosneft, is one of the largest in the region, with a production capacity of seven million tonnes per year, according to its official website.
A drone attack on another refinery in the region, Novokuibyshevsk, "was repelled without damaging the technological equipment", Azarov said.
The attacks came 24 hours after Russia unleashed one of its largest aerial barrages of the two-year conflict, hitting dozens of Ukrainian energy site and leaving more than a million temporarily without power.
Ukraine's air force said it had downed 31 of 34 Russian drones fire at its territory overnight, while Russia's defence ministry said it had intercepted 12 Ukrainian drones.
Ukraine, which has been facing a Russian offensive for over two years, has stepped up its attacks inside Russia in recent weeks, targeting energy sites in particular.
And Russia has also launched a barrage of what it calls "retaliatory" attacks, targeting Ukraine's energy sector and the capital Kyiv in recent days.