Critical infrastructure across Ukraine was pounded by more than a dozen Russian missiles on Saturday, the Ukrainian air force said, with several regions reporting strikes on energy facilities and power outages.

Ukraine's air force command reported that 33 missiles had been fired at Ukraine on Saturday morning, and that 18 of those had been shot down.

Russian air attacks have hit at least half of Ukraine's thermal generation capacity, causing billions of dollars of damage since October 10, though not all those power units have stopped working completely, Ukraine's Energy Minister Herman Halushchenko said on Friday.

Halushchenko told Reuters in an interview that Ukraine may need electricity imports to get through the winter after attacks that had struck 30-40 percent of power infrastructure and traders were already holding negotiations with suppliers.

Shortly after daybreak on Saturday, local officials in regions across Ukraine began reporting strikes on energy facilities and power outages as engineers scrambled to restore the ruined network. Governors advised residents to stock up on water in case of cut-offs.

Ukrainian presidential advisor Kyrylo Tymoshenko said that as of Saturday afternoon, more than a million people across Ukraine were without power, with 672,000 of those in the western region of Khmelnytskyi alone.

After the first wave of missiles hit early in the morning, air raid sirens rang out again nationwide at 11:15 a.m. local time (0815 GMT).

There has been no response from the Russian side on the claims of energy facility attacks.

On Saturday, pro-Russian authorities of the Kherson region urged residents to immediately leave Kherson and cross to the left bank of the Dnieper, TASS reported.

(With input from Reuters)