The bipartisan amendment, released late Monday, comes as the White House is deeply embroiled in a crisis over whether Trump's campaign team colluded with Russian officials to help sway the 2016 election in Trump's favor.
The measure would require a green light from Congress in the event sanctions on Russia are relaxed, suspended or terminated.
It would codify in law the sanctions imposed by executive decree by Barack Obama, especially against the Russian energy industry.
And it would impose new sanctions on "corrupt Russian actors," those implicated in serious human rights abuses or who supply weapons to Bashar al-Assad's regime in Syria, and people who conduct "malicious cyber activity" on behalf of the Russian state.
"I believe it's particularly significant that a bipartisan coalition is seeking to reestablish Congress as the final arbiter of sanctions relief -- no matter what the administration does -- considering that this administration has been too eager to put sanctions relief on the table," top Senate Democrat Chuck Schumer said Tuesday.
In addition to Russia's cyber-attacks that helped it interfere in the US elections, the reasons for tightening sanctions include responding to Russia's violation of Ukraine's and Crimea's territorial integrity, and its continuing aggression in Syria.
The amendment is being attached to an Iran sanctions bill aimed at punishing Tehran for its "continued support of terrorism." The measure is widely expected to pass Congress.
The Senate holds a procedural vote Wednesday and a final vote possibly this week. It then heads to the House of Representatives.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.