The Kremlin on Monday admitted "mistakes" in mobilizing hundreds of thousands of reservists to fight in Ukraine, amid angry protests and many Russians fleeing the country.
"There are cases where the decree has been violated," said the Kremlin spokesman, saying he hopes "mistakes will be corrected."
He further indicated that the authorities had not "made a decision" on closing the borders to men of military age.
With around 17,000 entries, Finnish border guards announced on Monday that they had recorded the busiest weekend of the year for Russian entries, twice as many since the announcement of Moscow's "partial" mobilization for the war in Ukraine.
Read alsoWar in Ukraine: sanctions, minorities, money ... how Putin seeks to mobilize fighters
This Monday, a man opened fire in a Russian army recruitment center, seriously injuring an officer who worked there, at a time of growing protests in Russia against the partial mobilization ordered to fight in Ukraine.
No indication was given of the motive for the crime.
The incident took place at a military commissariat in Oust-Ilimsk, a remote town in the Irkutsk region of Siberia, as the Kremlin is accused of seeking to prioritize mobilization in poor and isolated areas.
The Russian Investigative Committee said the suspect, a 25-year-old resident, had been arrested.
The victim is hospitalized in very serious condition.
Events in the regions
This incident comes as in places anger is mounting in Russia against the partial mobilization ordered on September 21 by President Vladimir Putin.
According to the NGO OVD-Info, more than 2,300 people have been arrested since this announcement during protest actions since this announcement.
Significant departures of Russians to neighboring countries have also been reported.
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Demonstrations, rush on plane tickets ... the "partial mobilization" goes badly in Russia
This weekend, protests took place in the Russian republic of Dagestan, a poor, multi-ethnic and Muslim-majority region of the Caucasus that has already paid a very heavy price in the conflict in Ukraine.
According to the specialized NGO OVD-Info, at least 100 people were arrested on Sunday in Makhachkala, the Dagestani capital.
Videos, published by Russian media, showed women attacking police during the protest.