A cloud of smoke rises after an explosion in Lviv, western Ukraine. AP

Russian forces pressed their assault on Ukrainian cities on Friday, hitting a building near a western city's airport with missiles, as world leaders pushed for an investigation of the Kremlin’s repeated attacks on civilian targets, including airstrikes on schools, hospitals and residential areas.

Lviv Mayor Andriy Sadovyi said on Telegram that several missiles hit a facility used to repair military aircraft and damaged a bus repair facility, though no casualties were immediately reported. The aircraft repair facility had suspended work ahead of the attack, the mayor said.

The missiles that hit Lviv were launched from the Black Sea, but two of the six that were launched were shot down, Ukrainian air force’s western command said on Facebook.

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Not far from the Polish border and well behind the frontlines, Lviv and the surrounding area has not been spared Russia's attacks, the worst of which killed nearly three dozen people last weekend at a training facility near the city. Meanwhile, the city's population has swelled by some 200,000 as people from elsewhere in Ukraine have sought shelter there.

Smoke could be seen rising from the western part of the capital Kyiv after an early morning barrage on Friday. There were no immediate reports of casualties or what had been damaged.

In city after city around Ukraine, hospitals, schools and buildings where people sought safety from the bombardment have been attacked. Rescue workers searched for survivors in the ruins of a theatre that served as a shelter when it was blown apart by a Russian airstrike in the besieged southern city of Mariupol. And in Merefa, near the northeast city of Kharkiv, at least 21 people were killed when Russian artillery destroyed a school and a community center, a local official said.

In the northern city of Chernihiv, dozens of bodies were brought to the morgue in just one day.

US Secretary of State Antony Blinken said Thursday that American officials were evaluating potential war crimes and that if the intentional targeting of civilians by Russia is confirmed, there will be "massive consequences.”

The United Nations political chief, Undersecretary-General Rosemary DiCarlo, also called for an investigation into civilian casualties, reminding the UN Security Council that international humanitarian law bans direct attacks on civilians.

She said many of the daily attacks battering Ukrainian cities "are reportedly indiscriminate" and involve the use of "explosive weapons with a wide impact area.” DiCarlo said the devastation in Mariupol and Kharkiv ”raises grave fears about the fate of millions of residents of Kyiv and other cities facing intensifying attacks.”

Associated Press