Mikhail Degtyarev, the lawmaker who proposed the bill, compared the dollar to a Ponzi scheme. He warned that the government would have to bail out Russians holding the U.S. currency if it collapsed.

“If the U.S. national debt continues to grow, the collapse of the dollar system will take place in 2017,” said Mr. Degtyarev, a member of the nationalist Liberal Democrat Party who was a losing candidate in Moscow’s recent mayoral election.

“The countries that will suffer the most will be those that have failed to wean themselves off their dependence on the dollar in time.