America and its allies will act “decisively” if Russia uses a tactical nuclear weapon in Ukraine, US national security adviser Jake Sullivan said on Sunday, reaffirming the Joe Biden White House’s previous response to mounting concerns that Vladimir Putin’s threats are in increased danger of being realized.

“We have communicated directly, privately and at very high levels to the Kremlin that any use of nuclear weapons will be met with catastrophic consequences for Russia, that the US and our allies will respond decisively, and we have been clear and specific about what that will entail,” Sullivan told CBS’s Face The Nation.

Sullivan said that the Russian leader Putin had been “waving around the nuclear card at various points through this conflict”, and it was a matter that Biden’s administration has “to take deadly seriously because it is a matter of paramount seriousness – the possible use of nuclear weapons for the first time since the second world war”.

In a separate interview with CBS, Ukraine president Volodymyr Zelenskiy said he was not certain that Putin was bluffing with nuclear threats. “Maybe yesterday it was bluff. Now, it could be a reality,” he said. “He wants to scare the whole world.”

The administration’s security chief said that Russia’s nuclear threat against Ukraine, including extending its nuclear umbrella over eastern parts of the country that are still being contested seven months after its invasion, would not deflect the US and its allies.

“We will continue to support Ukraine in its efforts to defend its country and defend its democracy,” Sullivan said, pointing to more than $15bn in weapons, including air defense systems, hundreds of artillery pieces and rounds of artillery, that the US has supplied to Ukraine.

He said that Moscow’s mobilization of troops was a “sham referenda in the occupied regions” that would not deter the US. “What Putin has done is not exactly a sign of strength or confidence – frankly, it’s a sign that they’re struggling badly on the Russian side,” Sullivan said.

But, Sullivan added, it is “too soon to make comprehensive predictions” about a collapse of Russian forces.

“I think what we are seeing are signs of unbelievable struggle among the Russians – you’ve got low morale, where the soldiers don’t want to fight. And who can blame them because they want no part of Putin’s war of conquest in their neighboring country?”

Sullivan continued: “Russia is struggling, but Russia still remains a dangerous foe, and capable of great brutality.” He alluded to mass burial sites containing hundreds of graves that Ukrainian forces found after recapturing Izium from Russia and said, “We continue to take that threat seriously.”

He added that the US, the International Atomic Agency and Ukraine nuclear regulators are working together to ensure there is no “melt-down” at the Zaporizhzhia nuclear plant in eastern Ukraine.

The Russians, he said, had been “consistently implying that there may be some kind of accident at this plant”.

Reactors at the plant, Sullivan said, had been put into “cold storage” to “try to make sure there is no threat posed by a melt-down or something else at the plant. But it’s something we all have to keep a close eye on.”

Separately, Sullivan said US criticism of a crackdown on mounting protests in Iran after the death in police custody of 22-year-old Mahsa Amini would not affect the administration’s offer to lift sanctions on Iran as part of the effort to reach a deal on nuclear enrichment.

“The fact that we are in negotiations with Iran on its nuclear program is in no way impacting our willingness and our vehemence in speaking out about what has been happening on the streets of Iran,” he said.

Last week, Biden told the General Assembly of the United Nations in New York that “we stand with the brave citizens and the brave women of Iran who right now are demonstrating to secure their basic rights”. The US president’s remarks came shortly after a defiant speech by Iranian President Ebrahim Raisi.

In his remarks on Sunday, Sullivan said the US had taken “tangible steps” to sanction the morality police who caused the death of Mahsa Amini.

“We’ve taken steps to make it easier for Iranians to be able to get access to the internet and communications technologies to talk to one another and talk to the world and we will do all that we can to support the brave people, the brave women, of Iran,” Sullivan said.

But Sullivan refused to be drawn out on whether the US would change its policy on lifting sanctions in exchange for a nuclear deal in light of the protests.

“We’re talking about diplomacy to prevent Iran from ever getting a nuclear weapon,” he said. “If we … succeed …, the world, America and its allies will be safer.”

But the pursuit of a nuclear deal, Sullivan said, “would not stop us in any way from pushing back and speaking out on Iran’s brutal repression of its citizens and its women. We can and will do both.”