A Russian missile strike in Ukrainian President Volodymyr Zelensky's hometown of Kryvyi Rih left three dead and dozens wounded on Tuesday, in an attack Kyiv warned would not go "unpunished".

The strike came hours after Russia said it had repelled a series of brazen cross-border raids by pro-Ukrainian militias, who burst into its territory and claimed to seize control of a village.

Rescuers in Kryvyi Rih could be seen evacuating wounded civilians from a burning multi-storey residential building in a video published by Kyiv's interior ministry.

"The Russian attack claimed the lives of three people," the governor of the central Dnipropetrovsk region, Sergiy Lysak, said on Telegram.

At least 44 people were injured, eight of whom were in serious condition including three children, he said in a later post.

Zelensky said a residential building nine storeys tall was hit and offered his condolences to those affected in his evening address.

"We will inflict losses on the Russian state in response -- quite rightly. They in the Kremlin must learn that terror does not go unpunished for them," he said.

'Not in control'

Hours earlier, Russia said it had suppressed a series of armed attacks by pro-Ukrainian militias on its border regions using heavy artillery fire.

Groups of pro-Kyiv volunteer fighters, made up of Russians who oppose the Kremlin, said earlier that they had broken into the Kursk and Belgorod regions bordering Ukraine. Moscow said it had responded with rockets and "flame-throwing".

"The village of Tyotkino, Kursk region, is completely under the control of Russian liberation forces," said the Freedom of Russia legion, a militia that claims to be made up of Russian citizens fighting on behalf of Ukraine, in a post on Telegram.

It published a video purporting to show a handful of Russian troops fleeing across a snowy field.

Moscow denied that the fighters had made ground, and later said it had repelled all incursions from its territory.

"Through the self-sacrificing actions of Russian servicemen, all attacks by Ukrainian terrorist formations have been repelled," Moscow's defence ministry said.

A spokesman for Ukraine's military intelligence, Andriy Yusov, said the fighters were not acting under orders from Kyiv.

But he said the attacks showed "the Kremlin is once again not in control of the situation in Russia."

In Russia's Belgorod region, a member of the territorial defence was killed and 10 civilians wounded during the incursion, regional governor Vyacheslav Gladkov said.

Kursk Governor Roman Starovoyt said there had been a shoot-out in his region.

And in the Bryansk region, further north, a resident was killed by a mine, governor Alexander Bogomaz said.

The Ukraine-based militias -- made up of Russian citizens who oppose Moscow's invasion and have taken up arms for Kyiv -- have claimed to be behind previous incursions into Russian territory.

The Russian Volunteer Corps and the Freedom of Russia Legion said they took temporary control of several settlements in the Belgorod region in May and June 2023 in a string of raids after breaking through a border checkpoint.

A spokesperson for the political wing of the Freedom of Russia Legion told AFP on Tuesday the latest attack was timed to coincide with Russia's March 15-17 presidential elections.

"This is not an election at all. It is the next stage of a usurpation of power, the formation of Putin's dictatorship under the guise of elections," spokesman Alexei Baranovsky said.

Major oil refinery

Earlier Tuesday, Kyiv launched one of its most significant drone strikes on Russia so far in the two-year war.

Two Russian energy sites, including one of the largest oil refineries, around 800 kilometres (500 miles) from the border, were hit overnight, Russian officials said.

Ukraine has previously justified attacks on Russian energy sites as legitimate targeting of infrastructure used to fuel the invasion. It did not claim responsibility for Tuesday's strikes on the refineries.

A major oil refinery in Kstovo, just outside the city of Nizhny Novgorod, was hit by a drone early on Tuesday morning, the regional governor said.

Russia's Lukoil energy giant, which owns the refinery and says it is one of the largest in Russia, said it had "temporarily suspended" operations there following an unspecified "incident".

Videos on social media showed a large blaze raging in a facility purported to be the refinery, with black smoke billowing into the sky.

Another drone crashed into a fuel depot and started a fire in Oryol, around 160 kilometres from the border, according to the regional governor.

Also on Tuesday, Russia's state news agencies cited the defense ministry as saying a Russian Il-76 military transport plane with 15 people on board had crashed in the Ivanovo region, around 200 kilometers (125 miles) east of Moscow, after an engine fire.