Human Rights Watch and Amnesty International were among organizations that had their offices raided by Russian authorities in Moscow.
Russian laws enacted in November list NGOs as foreign agents if they receive some of their funding from foreign governments.
Human Rights Watch called on Council of Europe Secretary-General Thorbjorn Jagland to pressure the Russian government over the law during his visit this week to Moscow.
The Russian government's crackdown on civil society is unprecedented and has created a profoundly hostile climate for human rights work," Europe and Central Asia Director Hugh Williamson said in a statement from Moscow.
The Russian Foreign Ministry warned against making "ideology-based" assessments of its internal affairs after the European Union expressed concern over the law this week, Russia news agency RIA Novosti reports.
Russian President Vladimir Putin defended the measure as part of an anti-corruption and transparency campaign.
Williamson said Putin's measure appears to be part of an effort by silencing "groups by tarnishing them as 'agents' for foreign governments."
Toddler uninjured after being knocked over by Obama family dog
Texas principal bans speaking Spanish, stirs controversy