Russia's defence ministry said the air strike on Sunday had destroyed a large amount of weapons supplied by foreign nations that were being stored at the sprawling training facility, and that it had killed "up to 180 foreign mercenaries".
Reuters could not independently verify the casualties reported by either side.
The attack on the Yavoriv International Centre for Peacekeeping and Security, a base just 25km from the Polish border that has previously hosted NATO military instructors, brought the conflict to the doorstep of the Western defence alliance.
Russia had warned on Saturday that convoys of Western arms shipments to Ukraine could be considered legitimate targets.
Britain said the incident marked a "significant escalation". White House national security adviser Jake Sullivan said any attack on NATO territory would trigger a full response by the alliance.
Regional governor Maksym Kozytskyy said Russian planes fired around 30 rockets at the Yavoriv facility and that some were intercepted. At least 35 people were killed and 134 wounded, he said.
Russian defence ministry spokesperson Igor Konashenkov said Russia had used high-precision, long-range weapons to strike Yavoriv and a separate facility in the village of Starichi.
"As a result of the strike, up to 180 foreign mercenaries and a large amount of foreign weapons were destroyed," he said.
The 360-square km facility is one of Ukraine's biggest and is the largest in the western part of the country, which has so far been spared the worst of the fighting.
Ukraine, whose aspirations to join NATO are a major irritant to Russian President Vladimir Putin, held most of its drills with Western countries at the base before the invasion. The last major exercises were in September.
In the weeks before Russia's February 24 invasion, the Ukrainian military trained there, but according to Ukrainian media all foreign instructors left in mid-February, leaving behind equipment.
"The dining room and dormitory were destroyed. So were the barracks," said Colonel Leonid Benzalo, an officer in the Ukrainian medical reserve who was thrown across the room by one of the blasts. "The most important thing is we're still alive," he told Reuters after treating the wounded there.
While Western nations have sought to isolate Putin by imposing harsh economic sanctions and have been supplying Ukraine with weapons, the United States and its allies are concerned to avoid NATO being drawn into the conflict.
"There are no NATO personnel in Ukraine," the NATO official said, when asked if anyone from the alliance was at the base.
Heavy fighting was reported on multiple fronts.
Air raid sirens wailed across the capital Kyiv and authorities said they were stockpiling two weeks worth of food items for the 2 million people who have not yet fled from Russian forces attempting to encircle the city.
Ukraine reported renewed air strikes on an airport in the west and heavy shelling on Chernihiv northeast of the capital.
An American journalist was shot and killed by Russian forces in the town of Irpin, northwest of Kyiv, and another journalist was wounded, the regional police chief said.
Seeking to up the ante on the increasingly sanctions-hit Russian economy, Ukrainian President Volodymyr Zelenskiy, in a Twitter post, called on US software firms Microsoft Corp and Oracle Corp and German business software group SAP to halt support services in Russia.
In eastern Ukraine, Russian troops were 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 British Defence Ministry said.
The city council in Mariupol said in a statement that 2187 residents had been killed since the start of the invasion. Reuters was not able to verify that toll.
Kharkiv, Ukraine's second-largest city, has suffered some of the heaviest bombardment.
In Chernihiv, northeast of Kyiv, firefighters rescued residents from a burning building after heavy shelling, video from emergency service - and verified by Reuters - showed.
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.