Officials say children were among the dead; Ukraine blames Russian air defences for civilian casualties.
Moscow has accused Ukraine of deadly air strikes on south-west Russia – with 20 people killed and more than 100 injured in Belgorod, near the border.
The regional governor said three children were among the dead in what was one of the deadliest attacks on Russia since it invaded Ukraine.
A Ukrainian security source insisted that only military infrastructure had been targeted in Saturday’s action.
The attacks follow Russian strikes on Ukraine on Friday, which killed 39.
Those strikes were described by Kyiv as Russia’s biggest missile bombardment of the war so far.
Moscow accused its neighbour of launching Saturday’s attack with multiple forms of weaponry – including Ukrainian Olkha and Czech-made Vampire rockets.
Speaking to the BBC, the Ukrainian security source said more than 70 drones had been launched against Russian targets, as a “response to Russia’s terrorist attacks on Ukrainian cities and civilians”.
Addressing the situation in Belgorod, they blamed the “incompetent work of Russian air defence” for civilian casualties – saying this was what caused falling fragments.
Russia’s president has been briefed on the attacks, his spokesperson said.
An urgent meeting of the UN Security Council in New York was held on Saturday at Russia’s request – with Russia saying it had asked the Czech representative to attend. The BBC is not able to verify the Russian claims that Czech ammunition was used.
During the meeting, Russia’s envoy to the UN, Vasily Nebenzya, accused Ukraine of carrying out a “deliberate, indiscriminate attack against a civilian target”.
His remarks were promptly refuted by Ukraine’s allies, with the French envoy saying that Ukraine was defending itself under UN laws, while others including the US and UK said President Vladimir Putin was responsible for Russian deaths by starting the conflict.
The UN assistant secretary-general, Mohamed Khiari, “unequivocally condemned” the attacks on both sides and said strikes against civilians and civilian infrastructure “violate international humanitarian law, are unacceptable and must end now”.
Video from one of the strikes – which the BBC has verified but chosen not to share – shows a pile-up of cars, some of which are on fire, and at least one person lying motionless on the road.
The sound of loud bangs and car horns can be heard throughout. Before thick black smoke obscures the scene, someone is seen running to assist the person lying on the road.
“Today, shelling by the armed forces of Ukraine has had the most severe consequences of the last two years,” Belgorod’s regional governor wrote in a Telegram post.
The Russian defence ministry said Kyiv was “trying to distract attention from defeats at the front, and is also wanting to provoke us”.
The statement added: “This crime will not go unpunished.”
Late on Saturday, the governor of Ukraine’s Kherson region said one person had been killed during Russian shelling of a residential building.
At the same time, Russian strikes injured 19 in the Ukrainian city of Kharkiv, the local government reported.
Russia launched six rocket attacks on the city, the head of Kharkiv’s regional administration said. He added that two children and a foreign national were among those injured.
The Russian defence ministry earlier said 13 missiles had been destroyed over the wider Belgorod region – and 32 drones had been shot down in the Bryansk, Oryol, Kursk and Moscow regions.
The Bryansk governor said two villages were targeted and a child had been killed.
Ukrainian media – citing intelligence sources – reported that a group of drones hit an electronics factory in that same region, saying the facility had been used to make Russian military equipment.
Moscow has repeatedly accused Ukraine of being behind drone strikes in recent months. Kyiv rarely admits to such attacks across the border, although it has carried out strikes like this before.
Russia’s massive bombardment of Ukraine on Friday killed 39 people and injured nearly 160, according to President Volodymyr Zelensky. Several cities were hit, including the capital, Kyiv.
Mayor of Kyiv Vitali Klitchsko said at least 16 people were killed in the city – making Friday the deadliest day so far for civilians in the capital.
An emergency meeting of the UN Security Council that same evening overwhelmingly condemned Russia’s renewed mass-bombing campaign in Ukraine and said attacks had to stop “immediately”.
Countries including the US, UK and France said hitting civilian infrastructure had violated the international rules of war.
“Rather than peace, Putin chose to mark this holiday season… with an unprecedented number of drone and missile attacks,” US representative to the UN John Kelly said.
Russia said Ukrainian air defences were to blame for causing damage to civilian buildings.