The Russian public has supported the bill, with 56% of respondents in a poll conducted by the Public Opinion Foundation (FOM) saying they backed the ban, RIA Novosti reported.
In 2010, an American woman sparked outrage after she sent her adopted son back to Russia alone on a one-way flight, saying the boy, then 7, had violent episodes that made her family fear for its safety.
Konstantin Dolgov, the Russian Foreign Ministry's special representative for human rights, said Wednesday on Twitter that Russians were "well aware of, and have pointed out more than once, the inadequate protection of adopted Russian children in the U.S." He also said the United States is one of three nations that have not signed the 1989 U.N. Convention on the Rights of the Child.
According to the U.N. Children's Fund, the United States is one of two nations -- the other being Somalia -- that has not ratified the convention. But the United States has signed the convention, thereby signaling its intent to ratify.
Anthony Lake, executive director of UNICEF, touted the importance of "inter-country adoption."
"While welcoming Prime Minister Dmitri Medvedev's call for the improvement of the child welfare system, UNICEF urges that the current plight of the many Russian children in institutions receives priority attention," he said.
He asked that Russia let children's "best interests" guide the "design and development of all efforts to protect children."
Groups such as Amnesty International and Human Rights Watch had urged Russian lawmakers to reject the bill.
"This bill hits back at Russia's most vulnerable children and could deprive them of the loving families they desperately need," Hugh Williamson, Europe and Central Asia director at Human Rights Watch, said last week.
John Dalhuisen, Amnesty International's Europe and Central Asia program director, has said that "this bill is frankly a childish response to the Magnitsky Act."