The move by six senators is the latest warning from Capitol Hill to the new administration over US-Russian relations.
On Wednesday, a group led by Sens. Lindsey Graham, R-South Carolina, and Ben Cardin, D-Maryland, plan to introduce legislation that would impose strict new congressional oversight and veto power over the Trump administration if it decided to lift sanctions on Russia.
The Russia Review Act would require the White House to submit a report detailing why it was seeking to lift sanctions, setting into motion a 120-day review period where Congress could vote to disapprove of easing the penalties on the country, according to a summary of the measure provided to CNN.
Sen. Marco Rubio, a member of the Senate Foreign Relations Committee, is cosponsoring the Graham-Cardin measure, along with Democratic Sens. Claire McCaskill of Missouri, Sherrod Brown of Ohio and Republican John McCain of Arizona.
Rubio said support is broad within the Senate to push back against the White House if it eased sanctions before Russia pulls out of Ukraine, potentially enough to overcome any Trump veto.
"I think if there was a real threat of lifting sanctions minus the respect for Ukrainian sovereignty and meeting those conditions, my sense is that we would have the votes to pass that in the Senate and we would be able to pass it with a veto-proof majority," Rubio told CNN.
The new measure comes as roughly a dozen senators from both parties are quietly lobbying their colleagues to endorse a separate bill that would impose a comprehensive set of sanctions against Russia, picking up new support for their effort, including a member of the GOP leadership team, Sen. Cory Gardner of Colorado.
The under-the-radar moves underscore the growing concern on the Hill that Trump's openness to Vladimir Putin could prompt the United States to rebuild diplomatic ties with Russia, despite Washington's furious opposition to a host of Russian actions, including its annexation of Crimea and alleged cyberattacks during the U.S. election. And it comes as lawmakers in both parties have pushed back at Trump's comments over the weekend, when he seemed to equate US military actions with violence spawned by Putin's government.
It is uncertain when votes over the bills could take place and if Senate Foreign Relations Chairman Bob Corker will schedule a vote in his committee. But the Tennessee Republican has been a sharp Putin critic and has urged the White House to keep the existing sanctions in place.
"Sen. Corker strongly supports keeping sanctions in place against Russia for its continued destabilizing behavior in Ukraine," said Corker spokeswoman Micah Johnson.
Cardin, the ranking Democrat on the Senate Foreign Relations Committee, told CNN he has had conversations with GOP leaders who "are very concerned about our relationship" with Russia.
Asked if either the sanctions bill or the new review act would get a veto-proof majority of 67 senators, Cardin said: "I think if this matter comes up for a vote, it would be pretty close to those numbers."
This story has been updated.