Overnight Russian strikes on Ukraine's Lviv region killed two people, its governor said on Sunday, as President Volodymyr Zelensky urged his nation to endure during its third Easter at war.

Ukraine is on the back foot as the Russian invasion grinds into its third year, suffering ammunition shortages on the front line and pleading for Western support to fend off relentless aerial attacks.

Russian cruise missiles targeted critical infrastructure in the western Lviv region, killing two people, governor Maksym Kozytsky wrote on Telegram.

He said one man had been killed after an "administrative building" was destroyed, and rescuers later found the body of another under the rubble.

National energy operator Ukrenergo said Russia also targeted high-voltage facilities in the south, forcing emergency shutdowns in the Black Sea city of Odesa and nearby areas.

"There is no night or day when Russian terror does not try to break our lives," Zelensky wrote in an Easter Sunday message to Ukrainians on social media after the air force reported downing nine missiles and nine drones overnight.

"But we defend ourselves, we endure, our spirit does not give up and knows that it is possible to avert death. Life can prevail," he said.

Moscow has intensified strikes on Ukrainian energy facilities in recent weeks, saying it is responding to attacks by Kyiv on Russian border regions.

Energy consumption restrictions remained in place in Ukraine's second city Kharkiv and Zelensky's hometown of Kryvyi Rig following earlier Russian attacks, Ukrenergo said on Sunday.