More than 60,000 Russian children have been adopted in the United States in the past two decades with Russia being the single biggest source of adopted children for years.
UNICEF estimates that there are about 740,000 children without parental custody in Russia, while only 18,000 Russians are now waiting to adopt a child.
The bill has angered many Russians who argue that it victimizes Russian orphans who will be robbed of the opportunity to get a family.
Putin on Thursday indicated his intention to endorse the measure.
"I still don't see any reasons why I should not sign it," he told a televised meeting, referring to the bill. He went on to say that he "intends" to sign it.
The president said U.S. authorities deny access to adopted Russian children and let Americans suspected of violence toward Russian adoptees go unpunished.
Critics of the bill have left dozens of stuffed toys and candles outside the parliament's lower and upper houses of parliament to express solidarity with Russian orphans.
Children rights ombudsman Pavel Astakhov on Wednesday said that 46 children who were about to be adopted in the United States would remain in Russia in case the bill comes into effect.
Astakhov on Thursday petitioned the president to extend the ban to other countries.
"There are huge money, dodgy people and semi-legal schemes for exporting children," Astakhov tweeted, explaining his decision.
The Russian parliament has approved the bill, which is part of a larger measure by lawmakers retaliating against a recently signed U.S. law calling for sanctions against Russians deemed guilty of human rights violations.
The U.S. State Department said on Wednesday that it regretted the Russian parliament's decision.
This program aired on December 27, 2012. The audio for this program is not available.