The Senate Foreign Relations and Banking Committee announced a deal that had the support of the committee's top Democrats and Republicans that's expected to attract wide bipartisan support.
The proposal would provide for a congressional review process if the executive branch eases current sanctions on Russia. And it 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."
The measure would also authorize assistance for European countries concerned about Russian aggression, and require a study on the "flow of illicit finance involving Russia and a formal assessment of US economic exposure to Russian state-owned entities."
The legislation is expected to be attached as an amendment to an unrelated bill involving sanctions on Iran.
Sen. Bob Corker, chairman of the Senate foreign relations committee, had previously been hesitant to take up a Russia sanctions bill in his committee. But he said last month that he wanted to see progress with Russia or else he would move a sanctions measure.
Despite mixed signals from the President and his administration this year over sanctions, a senior source on Capitol Hill said the White House is not fighting congressional efforts to push through the measure.
Sen. Ben Cardin, the top Democrat on foreign relations, expressed confidence Monday that Trump would sign off on it.
"I would be very, very surprised if the President vetoes this bill. Now he's surprised me on a lot of things. But we haven't passed a bill," he told reporters. "I find as we get to the finish line on these bills, every administration generally joins us...so I think we'll have the support of the administration. I'm confident about that."
On Tuesday, however, Secretary of State Rex Tillerson told a Senate committee he is reviewing the proposed sanctions, but is wary of action that could get in the way of the administration's efforts to make inroads with the Russian government on various issues.
"What I wouldn't want to do is close the channels off," Tillerson said.
He called for "flexibility" so the administration can "turn that heat up" when they see fit.
Provisions from the agreement match up with different bills that have already been introduced this year, including two by Cardin, who teamed up with Republican Sens. John McCain and Lindsey Graham.
The top members of the Senate banking committee -- Republican Sen. Mike Crapo and Democratic Sen. Sherrod Brown -- were also heavily involved.
Trump suggested in January before he was inaugurated that he would be open to lifting sanctions on Russia if they helped the US fight terrorists, though he said he'd keep the sanctions in place for "at least a period of time."
"If you get along and if Russia is really helping us, why would anybody have sanctions if somebody's doing some really great things?" he said in an interview with the Wall Street Journal.
The issue saw renewed attention after Yahoo News recently reported that Trump administration officials began developing plans to lift sanctions almost as soon as they took office.
Former State Department official Dan Fried, who was quoted in Yahoo's story, later clarified to CNN
that he did not have first-hand knowledge that the Trump administration would attempt to unilaterally relax Russia sanctions, but did reach out to some members of Congress because he was concerned by rumors he had heard from other officials that there was a possibility.
US Ambassador to the United Nations Nikki Haley emphasized last week the Trump administration has "stood strong" on the existing sanctions on Russia.
"We're going continue to call them out as we need to. At the same time, we are trying to see if we can have talks with them on how to better come in line in the Syrian conflict. We're working with them on counter-terrorism. But if we see Russia doing anything wrong, we're going to tell them," she said on CBS' "Face the Nation."