Sergei Mironov said the moratorium should continue until agreement has been reached with foreign countries on a set of adoption rules, the Russian news agency RIA Novosti reports.
"A special agreement should be signed guaranteeing that a state maintains proper control of adopted children," Mironov said.
His proposal follows problems with U.S. adoptions.
In the latest incident a 7-year-old Russian boy adopted by a U.S. woman was sent back to Moscow on grounds he had deep psychological problems.
A delegation of officials from the U.S State Department is planning a trip to Moscow next week to discuss adoptions.
Russia was the third largest source of U.S. adoptions in 2009 after China and Ethiopia.
China accounted for 3,001 adoptions, Ethiopia had 2,227 and Russia had 1,586.
Notable deaths of 2014 [PHOTOS]