Alexeyev became the subject of a criminal probe following remarks he made on Twitter criticizing the lawmaker who heads the children's issues panel in the lower house of parliament and her first deputy, the Russian news agency RIA Novosti reported.
MP Yelena Mizulina complained to authorities that Alexeyev posted offensive remarks on Twitter concerning Russia's recent introduction of a ban on "gay propaganda" to minors.
Under Russian law, promotion of same-sex relationships with children is illegal and punishable by fines of up to $153 for each offense.
The law has prompted LGBT activists to call for a boycott of the 2014 Winter Olympics in the Russian city of Sochi.
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