Video footage showed a devastated building with smoke pouring out of it and rescue workers looking on.

Much of the upper floor of what appeared to be a three-storey building had been badly damaged.

A covered corpse lay on the road nearby.

"Another (Russian) missile attack, another crime against humanity," Zelenskiy wrote on Twitter, describing the damage to a psychological clinic and a veterinary clinic in Dnipro.

"Only an evil state can fight against clinics.

"There can be no military purpose in this.

"It is pure Russian terror."

Regional governor Serhiy Lysak said a 69-year-old man had been killed.

"He was just passing by when the Russian terrorists' rocket hit the city," he said.

The governor said another man's body had been pulled out of the rubble and 21 of the 23 wounded had been taken to hospital.

Three were seriously hurt, he said.

The Ukrainian Defence Ministry called it a serious war crime under the Geneva Conventions, which set out how soldiers and civilians should be treated in war.

Russia did not immediately comment on the events in Dnipro, a large city that has frequently come under fire since Moscow began its full-scale invasion 15 months ago.

Moscow has dismissed allegations that its soldiers have committed war crimes and denies deliberately targeting civilians although its air strikes have often hit civilian infrastructure including residential buildings and medical facilities.

Moscow said earlier on Friday Ukraine had struck two regions in southern Russia with a rocket and a drone, but the missile was shot down by its air defences.

In the southern Russian city of Krasnodar, a blast damaged a residential and office building, officials said.

They did not say what caused the blast, although Russian media said it was a drone attack.

Unverified videos on social media showed a drone flying over the city.

Ukraine said its air defences had shot down 10 missiles and more than 20 drones launched by Russia in overnight attacks on Dnipro, the capital Kyiv and eastern regions.

Zelenskiy's office said a fire had broken out on the outskirts of the northeastern city of Kharkiv after an oil depot was hit twice, and that equipment for pumping oil products had been damaged.

After months of attacks on energy infrastructure, Russia has shifted the focus of its missile strikes to try to disrupt preparations for a Ukrainian counterattack, a senior military intelligence official said last week.

Attacks were increasingly targeting military facilities and supplies, he said.

Also on Friday, a senior ally of President Vladimir Putin warned the West was seriously underestimating the risk of a nuclear war over Ukraine, cautioning Russia would launch a pre-emptive strike if Ukraine gets nuclear weapons.

Russia, which has more nuclear weapons than any other state, has repeatedly said the West is engaged in a proxy war with Russia over Ukraine that could escalate into a much bigger conflict.

"There are irreversible laws of war," Russian Security Council deputy chairman Dmitry Medvedev was quoted as saying by Russian news agencies.

"If it comes to nuclear weapons, there will have to be a pre-emptive strike."

Allowing Ukraine nuclear weapons - a step no Western state has publicly proposed - would mean "a missile with a nuclear charge coming to them", Medvedev, who served as president from 2008 to 2012, was quoted as saying.

Australian Associated Press