She added that she was concerned that authorities may use the information to push activists to make incriminating statements about the organization.
Mr. Putin has accused the U.S. of fomenting anti-government protests in Russia as a means to weaken the country.
Kremlin-controlled television broadcasters, meanwhile, accused Golos of working to discredit the Russian elections on orders from Washington.
In October, Moscow ended the U.S. Agency for International Development’s two decades of work in Russia, saying the agency that funded Golos and other Russian NGOs was trying to influence Russian elections. The U.S. denied the claim.
Memorial head Oleg Orlov said the new law would give Russian authorities the right to carry out continuous audits and other inspections of groups that get money from abroad.
“They don’t even need to close an organization, they can effectively paralyze it with endless checks,” he said.
Mr. Orlov warned that registering as a foreign agent could expose an NGO to possible charges under another new law that made the definition of treason so loose as to brand any dissenter a traitor.
Asked to comment on activists’ intention to boycott the new law, the speaker of parliament’s lower house, Sergei Naryshkin, said that the law “must be unfailingly observed.”