Russian lawmakers have submitted a draft law to the State Duma that would impose sanctions on U.S. citizens accused of abusing the rights of Russians.
According to the draft, such citizens would be barred from entering Russia and have their Russian assets frozen.
The bill is expected to have its first reading this week.
Duma speaker Sergei Naryshkin indicated deputies were determined to pass the bill quickly.
"We will take action against the U.S. officials and citizens who harshly violate human rights," Naryshkin said.
"This very week the State Duma will consider a relative bill that has been written by the parliamentarians of all the four Duma factions."
Sergei Mironov of the A Just Russia party echoed Naryshkin's sentiments and said the bill was a "symmetrical" response to the U.S. Senate's passing of the so-called Magnitsky bill.
"Self-styling itself as the main actor on the international stage, the United States of America is meddling in the internal affairs of other countries and the Russian Federation in particular. We consider it unacceptable," Mironov said.
"I expect that tomorrow a relevant bill will be presented to the parliament and, as has been said, all the four factions of the State Duma will support it."
The deputy chairman of Federation Council, the upper house of Russia's parliament, Aleksandr Torshin, said later on December 10 that the Federation Council would approve the bill after it was passed by the Duma.
Torshin offered this advice to U.S. lawmakers: "Don't spit into the well, you may want to drink out of it."
The proposed measures come after the U.S. Senate passed the Magnitsky bill on December 6, which imposes visa bans and asset freezes on Russian officials accused of human rights violations.
The bill is expected to be signed by President Barack Obama and become law.
Russian Foreign Minister Sergei Lavrov said the role of parliaments is not to lecture other governments on how to behave.
"Similar attempts only bring intolerance and conflicts into the world affairs," he said. "The latest such example is the adoption of a bill by the United States Congress that introduces sanctions against Russian citizens based on a cynical guise."
The U.S. measure is named after Russian lawyer Sergei Magnitsky, who died in a Moscow prison in 2009 after implicating top officials in a scheme to defraud the government of $230 million.
He was repeatedly denied medical care and allegedly tortured during nearly a year in pretrial detention on what supporters say were trumped-up financial-crime charges.
Russia has prosecuted only one low-level prison official linked to his death, while promoting a number of others implicated in the case.
Rights activists accuse the Kremlin of failing to prosecute those responsible.
With reporting by AP, Interfax, and ITAR-TASS