Over 1.5 million people were without power in the southern Ukrainian city of Odessa on Saturday after a night attack by Russian "kamikaze drones", President Volodymyr Zelensky said.

The region's energy authority warned that repairs after the Friday strikes would take weeks, perhaps up to three months.

"After the night strike by Iranian drones, Odessa and other cities and villages of the region are in darkness," Zelensky said.

"As of now, more than one and a half million people in Odessa region are without electricity."

Kyrylo Tymoshenko, deputy head of the presidential administration, said only critical infrastructure including hospitals and maternity wards had access to electricity.

"The situation remains difficult, but is under control," Tymoshenko said.

The Black Sea port was a favourite holiday destination for many Ukrainians and Russians before President Vladimir Putin sent troops to pro-Western Ukraine on February 24.

Maksym Marchenko, the governor of the region, said Russia had attacked the city with "kamikaze drones" overnight.

"As a result of the strike, there is no electricity in almost all districts and communities of our region," he said.

Two drones were shot down by Ukrainian air defence units, Marchenko added.

On Friday, Kyiv said southern regions of the war-scarred country including Odessa were suffering the worst electricity outages days after the latest bout of systematic Russian assaults on the Ukrainian energy grid.

Russia fired dozens of cruise missiles at key infrastructure in Ukraine on Monday, piling pressure on the country's already ailing grid after repeated attacks.

Russia began targeting Ukraine's infrastructure following humiliating military defeats.

On Thursday, Putin vowed to keep battering Ukraine's energy grid despite an outcry against the attacks that have plunged millions into cold and darkness.