The Russian military said the attacks would not go unanswered and fired more artillery shells into Ukraine.
As Donald Trump prepares to take office as US president, Ukraine's military claims to have launched its largest airstrikes on Russian territory since the war began nearly three years ago.
Russia's Defense Ministry said on Tuesday it would retaliate against a massive overnight missile and drone attack and accused Ukraine of once again using missiles supplied by the United States and Britain.
The Russian military said most of the shells were shot down and the attacks targeted multiple cities and industrial sites.
Attacks were reported on the Russian cities of Saratov and Engels, with some damage to factories in the area. Some schools have been forced to switch to remote learning, and some airports have been forced to temporarily halt air traffic.
Ukrainian forces also struck the same area last week, claiming they hit an oil depot at a Russian bomber air base. The attack sparked a fire that was extinguished just a day before the latest attack.
The Ukrainian military said on Tuesday it had also struck Bryansk, Tula and Tatarstan, targeting a chemical plant that produces rocket fuel and ammunition for the Russian military.
At the end of November last year, Ukraine began to use US-made ATACMS ballistic missiles and British Storm Shadow missiles to attack targets in Russia for the first time.
Russia has said it wants to negotiate but will not give up its demands on Ukraine, warning that the move could seriously escalate tensions. Moscow also launched a new medium-range hypersonic ballistic missile called the Oreshnik in Ukraine and said it was ready for use again.
A day before Ukraine launched its latest attack on Russia, NATO Secretary-General Mark Rutte said Ukraine was not strong enough to "negotiate from a position of strength", something the incoming US president said he wanted to see.
During his re-election campaign, Trump said he would address the war before taking office. Former U.S. diplomat William Courtney said he had stopped mentioning the matter since his election and that his envoy to Ukraine had discussed the 100-day timetable.
“I think there are risks with any specific forecast because no one can completely know how things will play out, but President-elect Trump appears to be more supportive of Ukraine now than he was before the election,” an adjunct senior fellow at the agency RAND told Al Jazeera .
Courtney said that with its recent attacks on Russia, Ukraine may be trying to show Trump that "it has some fighting left that it can shift to Russia and have serious military repercussions."
Meanwhile, Russia continues to push deeper into eastern Ukraine, while Kiev persists with its military offensive in the Russian territory of Kursk, where this week it captured alive the first batch of North Korean soldiers fighting for Moscow.