Ukraine said foreign military instructors have previously worked at the base, but a NATO official told the Reuters news agency there were no personnel from the alliance there.
Regional governor Maksym Kozytskyy said Russian planes fired around 30 rockets at the Yavoriv International Center for Peacekeeping and Security, adding that some of the missiles were intercepted before they hit.
At least 35 people were killed and 134 wounded in the strike, Kozytskyy said in a statement.
The 360 square-km base, less than 25 km from the Polish border, is one Ukraine's biggest and the largest in the western part of the country.
Reuters said it was unable immediately to verify the report, while The Kremlin did not immediately reply to a request for comment on the missile strike so close to the border with NATO.
More than a dozen ambulances with sirens on were seen driving from the direction of the Yavoriv facility after the strike as black smoke rose from the area, Reuters reported.
"Russia has attacked the International Center for Peacekeeping & Security near Lviv. Foreign instructors work here. Information about the victims is being clarified," Ukraine’s Defence Minister Oleksii Reznikov said in an online post.
A Ukrainian defence ministry official told Reuters the ministry was still trying to establish if any foreign instructors were at the centre at the time of the attack.
Ukraine held most of its drills with NATO countries there before the invasion, with the last major exercises staged in September.
In the weeks before Russia’s invasion of Ukraine last month, the Ukrainian military trained at the facility, but according to Ukrainian media, all foreign instructors left the training ground in mid-February, while leaving all the equipment.
Sunday is day eighteen of the Russian invasion of Ukraine, which began on February 24.
While Western nations have sought to isolate Russia by imposing harsh sanctions, the United States and its allies are concerned to avoid the NATO military alliance being drawn into the conflict.
Sunday’s air strike brings the war close to the border of NATO member Poland.
It came as Ukraine officials on Sunday reported intense Russian attacks around the country. There were renewed air strikes on an airport in the west, heavy shelling on Chernihiv northeast of the capital Kyiv and attacks on the southern town of Mykolayiv, where nine people had been killed, according to Ukrainian authorities, as cited by Reuters.
Poland on Sunday reported it had admitted over 1.6 million people escaping the Russian invasion of Ukraine.
Source: Reuters, euronews.com, cnn.com, bbc.com