More than a dozen Russian missiles have pounded energy facilities and other infrastructure across Ukraine, with strikes causing blackouts in several regions.

President Volodymyr Zelensky says the Russian attacks struck on a “very wide” scale and has pledged his military will improve on an already good record of downing missiles with help from its partners.

At the same time, Russian occupation authorities in the southern Ukrainian city of Kherson urged civilians to leave immediately, citing what they called a tense military situation.

The Ukrainian military said it was making gains as its forces moved southward through Kherson region, taking over at least two villages it said Russian troops had abandoned.

Since October 10, Russia has launched devastating salvos at Ukraine’s power infrastructure, which have hit at least half of its thermal power generation and up to 40 per cent of the entire system.

Shortly after daybreak, officials in a swathe of regions reported strikes on energy facilities and power outages as engineers scrambled to restore the network. Governors advised residents to stock up on water.

Parts of Kyiv suffered power cuts into the evening. In one central district, shops were closed and traffic lights were off.

“The geography of this latest mass strike is very wide,” President Zelensky said on Saturday in his nightly video address, citing regions in western, central and southern Ukraine.

“Of course we don’t have the technical ability to knock down 100 per cent of the Russian missiles and strike drones. I am sure that, gradually, we will achieve that, with help from our partners. Already now, we are downing a majority of cruise missiles, a majority of drones.”

Ukrainian forces had downed 20 missiles and more than 10 Iranian-made Shahed drones on Saturday, he said.

The air force command earlier had said 33 missiles had been fired at Ukraine. Eighteen were shot down.

Reuters witnesses in the southern city of Mykolaiv reported a power cut over several hours, disrupting mobile phone signals.

In the southeastern city of Nikopol, which is regularly shelled from Russian positions across the Dnipro River, local authorities warned that air raid sirens would be switched off as a result of power cuts.

Instead, emergency vehicles driving around the city would warn of aerial threats, officials said.

President Zelensky said teams were working to restore power to affected areas. Presidential adviser Kyrylo Tymoshenko said earlier that more than a million people were without power after two morning air raid alerts.

Ukrainian presidential aide Mykhailo Podolyak said Moscow wanted to create a new wave of refugees into Europe with the strikes, while Foreign Minister Dmytro Kuleba said on Twitter the attacks constituted genocide.

Moscow has acknowledged targeting energy infrastructure but denies targeting civilians.

The battle for Kherson, which has been under Russian control for almost the whole of the eight-month war, appears to be reaching a critical juncture as advancing Ukrainian forces threaten to pin Russian troops along the Dnipro’s west bank.

The Russian-installed leader of the region said this week that Russia was planning to move an estimated 10,000 residents a day from Kherson and that Russia was preparing to take in residents in anticipation of Ukraine’s counterattack.

Despite the latest warning, the occupation authorities invited people still in the city on Saturday to attend an “evening of Russian literature, music and art” in Kherson’s Palace of Culture, with a book reading and orchestra playing.

Ukraine has imposed an information blackout from the Kherson front but Russian commander General Sergei Surovikin said this week the situation in Kherson was “already difficult” and Russia was “not ruling out difficult decisions” there.

In a briefing on Saturday, the Russian defence ministry said its forces had repelled a Ukrainian attempt to break through its line of control in the Kherson region.

Reuters could not independently confirm battlefield claims.

Kherson is the only provincial capital that Russia has captured intact and held since its February 24 invasion.

The Kherson region was one of four that President Vladimir Putin said last month that Russia was claiming “forever” as its own territory.