Lee specifically opposed a section of the amendment that appropriates $250 million to coordinate aid and counter cyberattacks in a handful of countries "vulnerable to influence."
During a "tele town hall" Wednesday night, where Lee answered questions in an online video chat, the senator said those funds could potentially go to nongovernmental groups that "have in the past spent money on politically divisive projects."
"I'm not about to authorize new spending $250 million or a lesser sum or a greater sum to do that again without adequate restraints in place to make sure that these international organizations aren't going to blow this money or aren't going to spend it in a way that's harmful to the interests of the American people," he explained.
The other senator voting no, Republican Rand Paul of Kentucky, told The Washington Examiner that he doesn't favor any new measures against Iran or Russia. The sanctions that passed Wednesday, he added, are inadequate, like "tweaking their nose."
Still, the measure passed 97-2. Democratic Sen. Chris Van Hollen of Maryland did not vote.
The Russia amendment include provisions to limit transactions and exports, put into law existing punishments laid out by the Obama administration and condemn the country's interventions in Ukraine and Syria.
Democrats succeeded in adding a measure that would restrict President Donald Trump whose administration has been entangled in investigations into ties to Russian officials from lifting the sanctions unless approved by Congress.
Many GOP senators applauded the measure as a way to penalize Russia for attacking American democracy.
"It's been eight months since Russia attacked our election, yet the Kremlin has only received a slap on the wrist," said Sen. John McCain, R-Ariz. "It's past time Russia pays a price for its brazen actions."
Closing two compounds and sanctioning a few individuals and spies as then-President Barack Obama did, he said, has not been enough. Though there's little dispute over Russia's interference in the election, questions remain over the purpose and extent of the meddling. U.S. intelligence reports have concluded that Russian President Vladimir Putin ordered a cyberattack with the intention of boosting Trump's chance to win.
The entire sanctions bill will likely pass the Senate by the end of the week; it's unclear whether or when the House would hear it.