Parliament expressed "deep concern" about human and political rights in Russia under President Vladimir Putin.
Putin backed a measure last year requiring NGOs to register as "foreign agents" if they received some of their funding from foreign governments.
Members of the European Parliament said Thursday they were "disappointed" by the NGO bill and had broader concerns about the negative consequences of the adoption of a federal law on "homosexual propaganda."
The lower house of the Russian parliament, the State Duma, passed a law criminalizing the promotion of same-sex relationships among minors.
A law that would impose jail terms for insulting religious beliefs was described Tuesday by state news agency RIA Novosti as a reaction to the prosecution of rock band Pussy Riot.
Pussy Riot member Maria Alyokhina is on a hunger strike while imprisoned. She was denied parole in May.
Members Alyokhina, Nadezhda Tolokonnikova and Yekaterina Samutsevicha were sentenced to two years in jail last year for hooliganism after performing a "punk prayer" protest against Russian President Vladimir Putin at a cathedral in Moscow.