In a rare moment of bipartisan unity, the Senate voted 97 to two to approve the sanctions, with only Republicans Mike Lee of Utah and Rand Paul of Kentucky voting against.
The Russia sanctions amendment was added to an Iranian sanctions bill on the Senate floor after a deal was struck earlier this week between the Republican and Democratic heads of the Senate Foreign Relations and Banking Committees.
The vote was overshadowed by Wednesday's shooting at a congressional Republican baseball practice
— two senators were there, Rand Paul and Jeff Flake of Arizona — but the Senate kept on its schedule, and the bill is expected to be passed by the end of the week.
The new Russia sanctions would create a congressional review process if the executive branch eases current sanctions. It also imposes new sanctions in a number of categories, including those "conducting malicious cyber activity on behalf of the Russian government" and "supplying weapons to the Assad regime."
Democrats and many Republicans have been pushing for the Senate to adopt a new Russia sanctions measure in response to Russia's interference in the 2016 US elections and after reports the Trump administration is considering easing sanctions on Moscow.
"This bipartisan agreement to stiffen sanctions is a significant step forward," said Sen. Jeanne Shaheen, a New Hampshire Democrat.
"We need this amendment because we have no time to waste," said Republican Sen. John McCain of Arizona. "The United States of America needs to send a strong message to Vladimir Putin and any other aggressor that we will not tolerate attacks on our democracy."
Republican senators said Tuesday they expected Trump to sign the bill, which will still need to be passed in the House before it goes to the President's desk.
Trump administration officials, however, have expressed some concerns with the package. Secretary of State Rex Tillerson told a Senate panel Tuesday he was wary of actions that could interfere with the administration's efforts to improve relations with Russia.
"What I wouldn't want to do is close the channels off," Tillerson said.
Senate Foreign Relations Committee Chairman Bob Corker of Tennessee was initially hesitant to pass a new Russia sanctions bill, but he played a key role in drafting the final language. He said Tuesday the administration should be supportive of the measure.
"I think the bill is a very, very strong signal to Russia, but it does provide the administration the flexibilities they need to conduct business," Corker told reporters. "I think we struck a very good balance."