The legislation also aims to prevent Trump from unilaterally easing pressure on Moscow. Meanwhile, the US president is reportedly being investigated for possible obstruction of justice.
The US Senate voted overwhelmingly on Wednesday for new sanctions punishing Russia for alleged meddling in the 2016 US election, and to force President Donald Trump to get Congress' approval before easing any existing sanctions.
It was introduced amid an intense focus in the US capital on relations with Russia, and investigations by the Department of Justice and congressional committees of whether Russia sought to influence the 2016 US elections to help elect Trump, and whether Trump associates colluded with Moscow as it sought to influence the election.
Moscow denies any such activity, which Trump has dismissed as sour grapes by the Democrats he defeated.
The Iran bill, including the Russia sanctions amendment, was expected to pass the Senate on Thursday or later on Wednesday.
To take effect, the measure would also have to pass the House of Representatives and be signed into law by Trump. If Trump objected, some of its backers said they expected enough congressional support to override a veto.
"Today the Senate has finally confronted Russia for interfering in our elections. This bipartisan amendment is the sanctions regime that the Kremlin deserves for its actions," said Democratic Senator Jeanne Shaheen, a leader of the push for the legislation.
The only two "no" votes on the Russia bill were from Republican Senators Mike Lee and Rand Paul.
The investigation into Russia's alleged interference in the 2016 US election took another turn, as the Washington Post reported Wednesday that Donald Trump is being investigated by special counsel Robert Mueller for possible obstruction of justice.
Mueller is investigating alleged Russian interference in the 2016 US presidential election and possible collusion with the Trump campaign. Former FBI Director James Comey told Congress last week he believes he was fired by Trump to undermine the agency's Russia probe.
The Washington Post, citing five people briefed on the requests who spoke on condition of anonymity, said Dan Coats, the director of national intelligence, Mike Rogers, the head of the National Security Agency, and Richard Ledgett, the former deputy director at the NSA, had agreed to be interviewed by Mueller's investigators as early as this week.
The obstruction of justice investigation into Trump began days after Comey was fired on May 9, according to people familiar with the matter, the Washington Post said.
Trump's legal team quickly denounced the report on Wednesday.
"The FBI leak of information regarding the President is outrageous, inexcusable and illegal," a spokesman for Trump's legal team, Mark Corallo, said.
A spokesman for Mueller's team declined to comment.
TRT World's Harry Horton has more on the story from Washington.