Russia's defence ministry said 15 other people were wounded in the shooting on Saturday, in Russia's southwestern Belgorod region that borders Ukraine, RIA news agency reported.
Two men gunned down a group who had volunteered to take part in the war.
The two assailants - nationals from an unspecified former Soviet republic - were shot dead, the ministry said. Some Russian independent media outlets reported that the number of casualties was higher than the official figures.
"A terrible event happened on our territory, on the territory of one of the military units," the governor of Belgorod region Vyacheslav Gladkov said early on Sunday.
"Many soldiers were killed and wounded ... There are no residents of the Belgorod region among the wounded and killed," Gladkov said in a video post on the Telegram messaging app.
The attack took place a week after a blast damaged a bridge in Crimea, the peninsula annexed by Russia from Ukraine in 2014. Earlier in the war, Russia's flagship in the Black Sea blew up and sank.
"During a firearms training session with individuals who voluntarily expressed a desire to participate in the special military operation (against Ukraine), the terrorists opened fire with small arms on the personnel of the unit," RIA cited a defence ministry statement as saying.
Just a day earlier, Putin said Russia should be finished calling up reservists in two weeks, promising an end to a divisive mobilisation that has seen hundreds of thousands of men summoned to fight in Ukraine and huge numbers flee the country.
Oleksiy Arestovych, an advisor to Ukrainian President Volodymyr Zelenskiy, said in a YouTube interview the attackers were from the Central Asian nation of Tajikistan and had opened fire on the others after an argument over religion.
Tajikistan is a predominantly Muslim nation, while around half of Russians follow various branches of Christianity.
The Russian ministry had said the attackers were from a nation in the Commonwealth of Independent States, which groups nine ex-Soviet republics, including Tajikistan.
The independent Russian news website SOTA Vision said the attack occurred in the small town of Soloti, close to the Ukrainian border and about 105km southeast of Belgorod.
Zelenskiy said on Saturday that Ukrainian troops were still holding the strategic eastern town of Bakhmut despite repeated Russian attacks while the situation in the larger Donbas region remained very difficult.
Russian forces have repeatedly tried to seize Bakhmut, which sits on a main road leading to the cities of Sloviansk and Kramatorsk. Both are situated in the Donetsk region.
In the 24 hours to Sunday morning, Russian forces targeted more than 30 towns and villages across Ukraine, launching five missile and 23 air strikes and up to 60 rocket attacks, the General Staff of Ukraine's Armed Forces said on Sunday.
In response, Ukraine's air forces carried out 32 strikes, hitting 24 Russian targets.
Fighting is particularly intense in the eastern provinces of Donetsk and Luhansk, and the strategically important Kherson province in the south, three of the four provinces Putin "annexed".
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