However, White House Communications Director Anthony Scaramucci said in an interview on CNN's "State of the Union" that President Donald Trump was still considering it.
"My guess is that he's going to make that decision shortly," Scaramucci said, noting that he had just started the communications job.
Scaramucci went on to say Trump was not sure
Russia was behind efforts to influence the 2016 election, despite the intelligence community's assessment.
But when asked about the bill on ABC's "This Week," Sanders said, "The administration is supportive of being tough on Russia, particularly in putting these sanctions in place."
She said the original legislation was poorly written, but that negotiations had produced a bill with changes the administration considered necessary.
"We support where the legislation is now," Sanders said.
A senior administration official told CNN later Sunday that the Congress had made changes the administration supported, pointing to the North Korea sanctions that were added to the bill and provisions addressing business-sector concerns.
"The administration supports sanctions on Russia and Iran and supports the direction the bill is headed, but won't weigh in conclusively until there is a final piece of legislation and no more changes are being made," the official said.
Administration officials had also lobbied, however, for changes to the provision that gives Congress veto power to block the administration from easing sanctions on Russia. Lawmakers rejected weakening that provision in the final agreement.
On Saturday, negotiators from the House and Senate said they had reached a consensus on legislation that would increase sanctions on Russia and allow Congress to stop the administration from offering Russia sanctions relief, should the administration try to do so.
Sen. Ben Cardin, a Democrat from Maryland, noted on "Fox News Sunday" that wide, bipartisan support for the measure meant even if Trump tried to veto the bill, Congress could pass it into law.
"If he vetoes the bill, we will override his veto," Cardin said.