They received official permission for a march next Sunday of up to 20,000 people, RIA Novosti reported.
Organizers say that the march, while it will follow the same route as two protests last year against President Vladimir Putin, is aimed only at the adoption law Putin signed in December.
"The organizers of the January 13 march are civil activists," Sergei Udaltsov, leader of the Left Front, said on Twitter.
While Putin and other officials say the law is a response to the deaths of 19 Russian children adopted in the United States in the past 13 years, it was also aimed at a recent U.S. law imposing economic sanctions on Russian officials involved in human rights abuses. The Magnitsky Act was named after Serge Magnitsky, a Russian human rights lawyer who died in police custody.
Russian orphanages remain overcrowded. About 45,000 children have been adopted by families in the United States since 1999, more than any other country, but polls show about 56 percent of Russians support the adoption ban.