The Russian Justice Minister, Alexander Konovalov was firmly against the possibility.

In 2013, it was reported that the Russian organization, The Right to Bear Arms, had only 1,000 members.  It was founded by Maria Butina, the 24 year old redhead pictured in the video and above.

Now we learn that Russian law has been changed to allow the civil population to carry lethal weapons for self defense.  From sputnicknews.com, on 18 November, 2014:

MOSCOW, November 18 (Sputnik) — Russia has updated its legislation to allow civilians to carry firearms for self-defense, according to an amended decree on lethal weapons that appeared Tuesday on the official database of Russian laws and legal documents.

It is not clear who exactly will be able to qualify to own pistols, for example.  It is not impossible to obtain a license to own a shotgun in Russia, but a person has to be a shotgun owner for several years before they may purchase a rifle.