Regional governor Maksym Kozytskyy said Russian planes fired around 30 rockets at the Yavoriv International Centre for Peacekeeping and Security, adding that some were intercepted before they hit.
The 360 square-km facility less than 25 km from the Polish border, is one Ukraine's biggest and the largest in the western part of the country.
A Ukrainian defence ministry representative told Reuters the ministry was still trying to establish if any foreign instructors were at the centre at the time of the attack.
Russia's invasion of Ukraine, launched by Putin on February 24, has sent more than 2.5 million people fleeing across borders and trapped thousands of people in besieged cities.
While Western nations have sought to isolate Putin by imposing harsh sanctions, the United States and its allies are concerned to avoid NATO being drawn into the conflict.
In eastern Ukraine, Russian troops are trying to surround Ukrainian forces as they advance from the port of Mariupol in the south and the second city Kharkiv in the north, the UK Defence Ministry said on Sunday.
Kharkhiv has suffered some of the heaviest Russian bombardment. Videos from residents show badly bombed buildings lining streets, burned out cars riddled with shrapnel holes and debris strewn across the ground.
The British intelligence also said Russian forces advancing from Crimea, which Russia annexed from Ukraine in 2014, were trying to circumvent Mykolaiv as they look to drive west towards Odesa.
Air raid sirens again woke residents in Kyiv on Sunday morning, hours after Ukrainian President Volodymyr Zelenskiy warned Russian forces they face a fight to the death if they try to occupy the capital.
Ukraine accused Russian forces of killing seven civilians, including one child, in an attack on women and children trying to flee fighting near Kyiv.
Moscow denies targeting civilians. It blames Ukraine for failed attempts to evacuate civilians from encircled cities, an accusation Ukraine and its Western allies strongly reject.
Polish President Andrzej Duda warned in an interview broadcast on Sunday that the use of chemical weapons in Ukraine by Russia would be a game changer and NATO would have to think seriously about how to respond.
The United States this week described renewed Russian accusations that Washington was operating biowarfare labs in Ukraine as "laughable" and suggested Moscow may be laying the groundwork to use a chemical or biological weapon.
Russian Deputy Foreign Minister Sergei Ryabkov said on Saturday the situation had been complicated by convoys of Western arms shipments to Ukraine that Russian forces considered "legitimate targets".
Any attack on such convoys before they reached Ukraine would risk widening the war.
Russian troops have destroyed 3,687 Ukrainian military infrastructure facilities so far, Russian Defence Ministry spokesman Igor Konashenkov was quoted by Russian news agencies as saying on Sunday. It was not possible to independently verify his statement.
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