The measure, approved earlier by the rubber-stamp parliament, reduces the penalty for violence against family members when it is the first such offence and does not cause serious injury, re-classifying it as an administrative misdemeanour punishable by a fine.
Previously such action was defined as battery, and was punishable by up to two years in jail.
Conservative proponents of the change argued it was not right to punish parents for disciplining their children and said the state should back out of private domestic affairs.
However the move sparked rare protest in Russia and critics said it would exacerbate the already-widespread problem of domestic abuse of women by making it even harder for them to get help through the legal system.
According to the state statistics agency, in 2015 there were 49,579 crimes involving violence in the family, of those 35,899 involving violence against a woman.
Kremlin spokesman Dmitry Peskov last month said that it is important to tell the difference between serious violence and "various manifestations of family relations."
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