The White House has said it is open to legislation toughening sanctions on Russia as momentum increased in the US Congress for stronger action.
Two US senators said they believe the legislation that allows for new sanctions against Russia would pass with enough votes to override a veto should President Donald Trump decide not to sign the bill.
Republicans and Democrats reached agreement allowing new sanctions targeting Russia, Iran and North Korea in a bill that would limit any potential effort by Mr Trump to try to lift sanctions against Russia.
"We support where the legislation is now and will continue working with the House and Senate to put those tough sanctions in place on Russia until the situation in Ukraine is fully resolved and it certainly isn't right now," White House press Secretary Sarah Sanders told ABC's "This Week with George Stephanopoulos" programme.
Many politicians hope the bill will send a message to Mr Trump to keep a strong line against Russia.
"I think (it) will pass probably overwhelmingly again in the Senate and with a veto-proof majority," Senator John Thune, a member of the Republican leadership, said on "Fox News Sunday."
Senator Ben Cardin, the top Democrat on the Senate Foreign Relations Committee, said the bill has "broad support in the Senate and in the House."
"If (Trump) vetoes the bill, we will override the veto," Mr Cardin said.
In recent weeks, officials from Mr Trump’s administration have met with politicians to argue against parts of the Senate version of the bill, including the requirement that Mr Trump obtain Congress' permission before easing sanctions.
The Countering Iran's Destabilizing Activities Act, which was passed by the Senate a month ago, was held up in the House of Representatives after Republicans proposed including North Korea sanctions in the bill.
In Brussels, the European Union has sounded an alarm about the US moves to step up sanctions on Russia, urging Washington to coordinate with its Group of 7 partners.
The European Commission, the EU's executive body, warned that there could be "wide and indiscriminate" unintended consequences, notably on the EU's efforts to diversify energy sources away from Russia.