Engineers worked round the clock to restore power on Monday to households in two Ukrainian cities -- Kharkiv and Odesa -- and officials warned that damage caused by repeated Russian strikes on energy infrastructure could take years to repair.

In Kharkiv, Ukraine's second largest city and a frequent target of Russian strikes, regional governor Oleh Synehubov said air defence units had downed at least eight drones in an evening attack.

Earlier, Synehubov told residents after a meeting of municipal and energy officials that repairs "were not a task of just a few weeks, or even months".

"The enemy has caused significant damage ad the restoration process may take quite some time," Synehubov wrote on the Telegram messaging app. "Specialists are working on sites around the clock. We are bringing in experts from other regions."

Odesa regional governor Oleh Kiper reported an evening missile attack on his Black Sea port city, with casualties confined to three injured.

Kiper said more than 300,000 residents were without power in the early evening.

President Volodymyr Zelenskiy said in his nightly video address that there had been strikes on energy infrastructure in Odesa and in Mykolaiv to the northeast and urged residents of Kharkiv to look after themselves and their neighbours.

Volodymyr Kudrytskyi, head of Ukrenergo, which operates Ukraine's transmission lines, said efforts were being made to eliminate energy shortfalls in the southern region.

But the situation, he said, was the most critical in Kharkiv "where the enemy with ballistic missiles has been trying to destroy all sites of trunk lines supplying the city".

Some 275,000 residents were without power, he said.

Ukraine's top private energy provider DTEK said earlier that emergency power cuts were introduced in Odesa after a Russian air attack damaged a high-voltage facility.

Four drones were shot down in the earlier attack on Odesa and Mykolaiv, local officials said.

(Reporting by Lidia Kelly in Melbourne and Ron Popeski; Editing by Stephen Coates, Toby Chopra and Michael Perry)