Ten people including a child were killed and 45 injured by Ukrainian strikes on targets in the centre of the Russian provincial capital of Belgorod on Saturday, according to Russia.
The Russian defence ministry also said it had destroyed dozens of missiles and drones fired into its territory by Ukraine.
The Kommersant newspaper cited a source close to the Russian Investigative Committee as saying missiles fired from a multiple rocket launcher in Ukraine's Kharkov region had hit a skating rink, a shopping centre, residential buildings and a car.
Kyiv has not commented on the reports.
The attacks follow Russian strikes on Ukraine which killed 39 people.
Ukrainian news outlet RBC-Ukraine quoted sources as saying Ukrainian forces had struck military targets in Belgorod in response to the bombardment the previous day.
Ukrainian officials described the attacks on Kyiv, Odesa, Dnipro, Kharkiv and Lviv as the worst aerial bombardment since the start of the war in February 2022.
“Works to clear up the consequences of yesterday's Russian attack are still underway. Almost 120 cities and villages, hundreds of civilian objects have suffered," Ukrainian president Volodymyr Zelensky said.
Mr Zelensky said 39 people were killed and 159 injured in the strikes that involved different types of ballistic and cruise missiles and Iranian-made drones.
Ukrainian air defence said it shot down 87 Russian missiles and over 30 drones.
In the capital Kyiv, at least 16 people were killed, the largest civilian death toll in the city during nearly 22 months of the war, said mayor Vitali Klitschko.
The city announced a day of mourning for the victims on January 1.
Klitschko said rescuers were continuing to pick through rubble in Kyiv where a warehouse and several residential and commercial buildings were hit.
Rescue efforts continued in other cities and villages in the centre, south, and west of the country, local officials said.
Local authorities also raced to help repair thousands of smashed windows in residential buildings and to restore heating, after power was knocked out in some areas.
