Russian missiles pounded Ukrainian energy and other facilities on Saturday, causing blackouts in various regions, Kyiv said, while Russian authorities in the southern city of Kherson urged civilians to evacuate.

Ukrainian President Volodymyr Zelenskiy said the Russian attacks had struck on a "very wide" scale. He pledged his military would improve on an already good record of downing missiles with help from its partners.

With the war about to start its ninth month and winter approaching, the potential for freezing misery loomed as Russia continued to attack Ukraine's power grid.

In Kherson, a target for Ukraine's aggressive counterattack, occupying Russian authorities instructed civilians to get out.

"Due to the tense situation at the front, the increased danger of massive shelling of the city and the threat of terrorist attacks, all civilians must immediately leave the city and cross to the (east) bank of the Dnipro!" they posted on Telegram.

Thousands of civilians have left Kherson after warnings of a Ukrainian offensive to recapture the city.

At Oleshky on the opposite bank of the Dnipro, Reuters saw people arriving by river boat from Kherson, loaded with boxes, bags and pets. One woman carried a toddler under one arm and a dog under the other.

"I really didn't want to (leave), I'm still in work," one resident said. "We wanted to stay here in the region, but now we don't know."

Ukraine's military said it was making gains as its forces moved south through the region, taking over at least two villages it said Russian troops had abandoned. Kherson links Ukraine to the Crimean Peninsula, which was annexed by Russia in 2014.

Deputy Prime Minister Iryna Vereshchuk said on Telegram: "Kherson region! Just a little bit more. Hang in there. The Ukrainian Armed Forces are at work."

Since October 10, Russia has launched devastating salvos at Ukraine's power infrastructure, hitting at least half its thermal power generation and up to 40 percent of the entire system.

Officials in a swathe of regions on Saturday reported strikes on energy facilities and power outages as engineers scrambled to restore the network. Governors advised residents to stock up on water.

More than a million people were without power, said presidential adviser Kyrylo Tymoshenko. Parts of Kyiv suffered power cuts into the evening, and a city official warned strikes could leave Ukraine's capital without power and heat for "several days or weeks".

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. (Reuters)