"To ratify the agreement on the extension of the Strategic Arms Reduction Treaty (New START) between the Russian Federation and the United States of America of April 8, 2010," the bill says.
The New START is proposed to be extended for 5 years, until February 5, 2026, according to accompanying documents to the draft ratification agreement.
It is assumed that the law will come into force on the day of its official publication.
According to Leonid Slutsky, the head of the State Duma International Affairs Committee, the Russian parliament's lower house will consider the draft agreement on the extension of the Strategic Arms Reduction Treaty at a plenary session on Wednesday.
The head of the upper house's international affairs committee, Konstantin Kosachev, said that he expected the Federation Council to ratify the agreement on Wednesday.
"I hope that we will be in time, because no further plenary sessions are planned until February 5," Kosachev told Sputnik.
Earlier in the day, Russian President Vladimir Putin and US President Joe Biden held a phone conversation.
According to the Kremlin statement, Putin congratulated Biden on the beginning of his work as US president and noted that "the normalization of relations between Russia and the United States would meet the interests of both countries and, given their special responsibility for maintaining security and stability in the world, the entire international community".
Putin and Biden expressed satisfaction with the exchange of notes on reaching an agreement on the extension of the New START treaty, the Kremlin said.
Speaking on behalf of Washington, White House Press Secretary Jen Psaki told reporters that the two leaders discussed an extension of the Strategic Arms Reduction Treaty as well as other bilateral issues.
"[Biden] called President Putin this afternoon with the intention of discussing our willingness to extend New Start for five years," Psaki said.
Later in the day, the White House said in a statement that Putin and Biden during their phone call on Tuesday agreed to examine strategic stability talks on a number of arms control and security matters.
"They discussed both countries’ willingness to extend New START for five years, agreeing to have their teams work urgently to complete the extension by February 5," the readout said. "They also agreed to explore strategic stability discussions on a range of arms control and emerging security issues."
New START has been in force since 2011, and is due to expire on February 5. It is the only legally-binding agreement on nuclear arms control that remains between Russia and the United States.
The treaty limits each country's nuclear arsenal to 700 intercontinental ballistic missiles, 1,550 nuclear warheads and 800 launchers.