Russia will face “catastrophic consequences” if it deploys nuclear weapons in Ukraine, the US has warned Kremlin officials.

Jake Sullivan, the US national security adviser, said on Sunday night (local time) that the US had “communicated directly, privately to the Russians at very high levels” how it would respond if Russian President Vladimir Putin carried out the nuclear strike threat he made during an address last week.

“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 programme.

Sullivan did not describe the nature of the planned response but said the US had privately “spelled out in greater detail exactly what that would mean” to Moscow.

It came as Putin’s foreign minister said on Sunday that annexed areas of Ukraine would be protected like Russian territory. Referendums in those areas are continuing, with Ukrainians under pressure from armed Moscow forces to cast their ballots.

Some of Putin’s allies, including the speaker of the State Duma, publicly broke ranks on Sunday to criticise the way in which conscripts are being recruited, amid reports of elderly and ill men being drafted after the Russian President announced a partial mobilisation order.

Putin made the nuclear threat in an address when he said Russia had “various weapons of destruction” at its disposal and would use “all the means available”, before adding that he was not “bluffing”.

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While the threat is seen by some as an attempt to assert control after a series of embarrassing defeats in Ukraine, Nato’s nuclear powers have started ramping up vigilance and deterrence.

In a separate interview on Sunday, Sullivan said Putin’s nuclear threats were a “matter that we have to take deadly seriously”.

Military analysts believe Putin could use Russia’s military doctrine, which allows it to use nuclear weapons to defend its territory, to reframe the conflict in Ukraine as defensive.

Sergei Lavrov, Russia’s veteran foreign minister, said on Sunday that the Kremlin could use nuclear weapons to defend occupied Ukrainian territories, if annexed following referendums.

Russian forces have only been able to coerce one in five residents of occupied Melitopol to vote in a sham annexation referendum despite the threat of violence, its exiled mayor has said.

Since voting began on Friday, Russian officials have been going door-to-door in occupied regions flanked by gunmen to give out ballot papers and identify voters.

Ukrainians living under occupation have been warned their families would be massacred if they refuse to take part.

Despite the threats, Ivan Fedorov, Ukraine’s elected mayor of Melitopol, said: “Our citizens haven’t taken part in this fake referendum … after three days Russia has only been able to find just 20% of people to vote. Nobody wants to vote, nobody wants to say yes to the Russian referendum.”

Of those forced to cast a vote, he said “90%” had voted against Russia’s occupation becoming permanent.

In the occupied regions of Ukraine, Moscow has introduced the rouble and issued Russian passports. Ballots are being held, and are expected to continue until Tuesday, in Russian-controlled parts of the Kherson, Luhansk, Zaporizhzhia and Donetsk regions.

Melitopol, in Ukraine’s southern Zaporizhzhia region, had a pre-war population of about 150,000 and is one of the largest cities to fall under Russian control since the start of the war.

In the build-up to the vote, pro-Moscow officials blocked evacuation routes to Ukrainian-held territory, only allowing women and children to flee to occupied Crimea, Fedorov said.

Fedorov said men of fighting age had been blocked from leaving altogether, raising the prospect of them being forcibly drafted into Russian-backed armed forces.

More than 60,000 people still reside in the city, without the support of Ukraine’s government.

“The city’s been fully occupied for the last seven months. Many thousands of citizens stay in Melitopol … and we can’t give them support or safety guarantees,” Fedorov said.

He urged Ukraine’s European and US allies to ignore Moscow’s threats of nuclear blackmail and deliver more weapons to Kyiv.

“As a reaction to these fake referendums, we await more weapons and heavy military equipment,” he said.

We’ve shown the world how our military can defend the land, but also our values, not just Ukrainian values but European, democratic values.”

Meanwhile, Ukraine’s President Volodymyr Zelensky, confirmed on Sunday that Kyiv had received high-powered air-defence systems for the first time from the US. The National Advanced Surface-to-Air Missile System (NASAMS) was promised by Washington last month.

Zelensky told CBS the shipment had been received but added: “Believe me, it’s not even nearly enough to cover the civilian infrastructure, schools, hospitals, universities, homes of Ukrainians.”