Sullivan's remarks represented the latest American warning following the thinly veiled nuclear threat made by Vladimir Putin last Wednesday in a speech in which the Russian president also announced his country's first wartime military mobilization since World War Two.
"If Russia crosses this line, there will be catastrophic consequences for Russia. The United States will respond decisively," Sullivan told NBC's "Meet the Press" program.
Sullivan did not describe the nature of the planned U.S. response in his comments on Sunday but said the United States has privately to Moscow "spelled out in greater detail exactly what that would mean." Sullivan said that the United States has been in frequent, direct contact with Russia, including during the last few days to discuss the situation in Ukraine and Putin's actions and threats.
U.S. President Joe Biden in a speech at the United Nations General Assembly in New York on Wednesday accused Putin of making "overt nuclear threats against Europe" in reckless disregard for nuclear nonproliferation responsibilities.
Russia also is staging a referendum in four eastern Ukrainian regions with the goal of annexing territory that Russian forces have taken during their invasion of Ukraine launched in February. Ukraine and its allies have called the referendums a sham designed to justify an escalation of the war and Putin's mobilization drive after recent battlefield losses.
By incorporating the areas of Luhansk, Donetsk, Kherson and Zaporizhzhia into Russia, Moscow could portray attacks to retake them as an attack on Russia itself, a warning to Ukraine and its Western allies.
After suffering setbacks on the battlefield, Putin is mobilizing 300,000 troops while also threatening to use "all available means" to protect Russia.
"This is not a bluff," Putin said in the remarks viewed on the world stage as a threat on the potential use of nuclear weapons.
Sullivan said on Sunday: "Putin remains intent ... on wiping out the Ukraine people that he does not believe have a right to exist. So he's going to keep coming and we have to keep coming with weapons, ammunition, intelligence and all the support we can provide."
(Reporting by Richard Cowan and Hannah Lang; Editing by Will Dunham)
By Richard Cowan