Russia said on Saturday that a Ukrainian strike killed at least 14 people and injured 108 in the city of Belgorod, a day after Russian strikes killed dozens in Ukraine.

Belgorod lies about 30 kilometres from the border with Ukraine and has been repeatedly targeted by what Russia says is indiscriminate shelling by Kyiv's forces.

Unverified footage showed debris strewn across the street and smoke billowing from burnt-out cars in the city's centre, while a large blast can be heard in dashcam footage posted on social media.

"According to updated information, 12 adults and two children were killed in Belgorod. Another 108 people, including 15 children, were injured," Russia's emergencies ministry said.

President Vladimir Putin has been briefed on the incident, the Kremlin said, while the Russian defence ministry warned the attack would "not go unpunished."

The attack came as rescuers in Ukraine continued to search through rubble on Saturday after Russian strikes killed at least 39 people the day before, in one of the fiercest attacks since the early days of the conflict.

Schools, a maternity hospital, shopping arcades and blocks of flats were all among the buildings hit in Friday's barrage, which triggered international condemnation.

Ukraine's military estimated Russia had launched 158 missiles and drones on Ukraine and 114 of them had been destroyed.

Air force spokesman Yuriy Ignat said that this was a "record number" of missiles and "the most massive missile attack" of the conflict, excluding the early days of constant bombardment.

"Work is still underway to eliminate the consequences of yesterday's Russian attack," Ukrainian President Volodymyr Zelenskyy said.

January 1 will be declared a day of mourning in the capital Kyiv, where at least 16 people were killed, Mayor Vitali Klitschko said. (AFP)