Russian President Vladimir Putin said this week that Moscow would accept any outcome of referendums in Donbas and Russia-held territories and would spare no means to defend its territorial integrity.
Sullivan told ABC News on Sunday that the White House had taken Putin's warning seriously.
"We have communicated directly and privately to the Russians at very high levels that there will be catastrophic consequences for Russia if they use nuclear weapons in Ukraine," he said.
The White House official claimed Russia understood well what it would face "if they went down that dark road." He added that the US was planning for every contingency and would respond decisively to Russia.
Russian lawmakers reacted with surprise to Washington's warning. Deputy security committee chair Anatoly Vyborny told Sputnik that the Americans were "escalating things to save their face."
"Russia never said it was going to use nuclear weapons. It is unclear what they meant by these accusations," he said.
Oleg Morozov, a member of the ruling United Russia party in the lower-house State Duma, told Sputnik that the US wanted to ratchet up tensions to justify additional supplies of lethal aid for Ukraine.
"It is not about us actually using nuclear weapons. They understand that there is no need to do it. But they want to convince the world that the nuclear threat is coming from Russia," he explained.