Russia "launched an air strike on the International Centre for Peacekeeping and Security", the head of the Lviv regional administration, Maksym Kozytsky, said on his verified Facebook page.

"I have to announced that, unfortunately, we have lost more heroes: 35 people died as a result of the shelling of the International Peacekeeping and Security Centre," Kozytsky later wrote on Telegram, updating an initial toll of nine.

"134 more with injuries of varying severity are in a military hospital," he added, saying the information on the toll was still being updated.

Fires at the base have been almost fully extinguished and pyrotechnics experts were examining the debris, the governor said.

The military base in Yavoriv, located some 40 kilometres (25 miles) northwest of the city, was a training centre for Ukrainian forces with foreign instructors, including from the United States and Canada.

It was also a hub for joint exercises involving Ukrainian soldiers and NATO allies.

Ukrainian Defence Minister Oleksiy Reznikov said "foreign instructors work here", although it was unclear whether any were present during the attacks.

Foreign troops left Ukraine shortly before Russia launched an invasion of its pro-Western neighbour on February 24.

The United States said on February 12 that it withdrew 150 of its instructors from Ukraine.

Reznikov condemned the bombardment as a "new terrorist attack on peace & security near the EU-NATO border", calling for the imposition of a no-fly zone.

"Action must be taken to stop this. Close the sky!" he wrote.

Cruise missiles were fired from Russian planes located over the Black Sea and the Sea of Azov, the regional governor said.

Washington on Saturday authorised $200 million in additional military equipment for Ukraine.

Russia the same day warned that its troops could target supplies of Western weapons to Ukraine.

Many Ukrainians have fled to relative safety in Lviv since the launch of Russia's invasion.

A short drive from EU member Poland, the city is also a transit hub for those leaving Ukraine.

Separately, the mayor of Ivano-Frankivsk in western Ukraine said the city's airport was targeted in a strike.

"Our morning in Frankivsk began with explosions. This is already the third strike on Frankivsk. They hit the airport," mayor Ruslan Martsinkiv said on Facebook.