"This bill will impose targeted sanctions on Russian officials who are involved in open violations of international law, including the recent poisoning of opposition leader and anti-corruption activist Alexei Navalny," the statement said.
The bill also provides for the US administration to submit a financial report to Russian President Vladimir Putin and his entourage, as well as to check for Russia's violation of American laws banning the use of chemical and biological weapons.
In addition to Rubio, the initiative was supported by Senator from the Republican Party Mitt Romney, as well as Democrats Chris Koons, Ben Cardin and Chris Van Hollen.
Earlier, the Kremlin noted the US sanctions dependence after the statement of the US Secretary of State Mike Pompeo about Washington's plans to create a coalition against Nord Stream 2 due to the situation with Navalny.
On September 17, the European Parliament adopted a resolution urging to find and freeze the European assets of those involved in Navalny's investigations.
Russian Foreign Minister Sergei Lavrov, in turn, stressed that Russia will not leave unanswered new Western sanctions if they are introduced.
On September 2, Germany announced that the tests conducted revealed a substance from the Novichok group in Navalny.
The Kremlin noted that no toxic substances were found in Navalny's body before he was taken to Berlin.