(Adds details on voting in referendums)
Third day of voting in referendums on joining Russia
Moscow warned not to cross nuclear line after Russian threats
Ukraine says shelling continues, Zelenskiy claims battle success
Police, opponents of Russian mobilization clash in Dagestan
By Tom Balmforth
KYIV, Sept 25 (Reuters) - The United States warned on Sunday of "catastrophic consequences" if Moscow uses nuclear weapons in Ukraine, after Russia's foreign minister said regions holding widely-criticised referendums would get full protection if annexed by Moscow.
Votes were staged for a third day in four eastern Ukrainian regions, aimed at annexing territory Russia has taken by force. The Russian parliament could move to formalise the annexation within days.
By incorporating the areas of Luhansk, Donetsk, Kherson and Zaporizhzhia into Russia, Moscow could portray efforts to retake them as attacks on Russia itself, a warning to Kyiv and its Western allies.
U.S. National Security Adviser Jake Sullivan said the United States would respond to any Russian use of nuclear weapons against Ukraine and had spelled out to Moscow the "catastrophic consequences" it would face.
"If Russia crosses this line, there will be catastrophic consequences for Russia," Sullivan told NBC's "Meet the Press" television program. "The United States will respond decisively."
The latest U.S. warning followed a thinly veiled nuclear threat made on Wednesday by President Vladimir Putin, who said Russia would use any weapons to defend its territory.
Foreign Minister Sergei Lavrov made the point more directly at a news conference on Saturday after a speech to the U.N. General Assembly in New York in which he repeated Moscow's false claims to justify the invasion that the elected government in Kyiv was illegitimately installed and filled with neo-Nazis.
Asked if Russia would have grounds for using nuclear weapons to defend annexed regions, Lavrov said Russian territory, including territory "further enshrined" in Russia's constitution in the future, was under the "full protection of the state".
British Prime Minister Liz Truss said Britain and its allies should not heed threats from Putin, who had made what she called a strategic mistake as he had not anticipated the strength of reaction from the West.
"We should not be listening to his sabre-rattling and his bogus threats," Truss told CNN in an interview broadcast on Sunday.
"Instead, what we need to do is continue to put sanctions on Russia and continue to support the Ukrainians."
Ukraine and its allies have dismissed the referendums as a sham designed to justify an escalation of the war and a mobilisation drive by Moscow after recent battlefield losses.
Russian news agencies quoted unidentified sources as saying the Russian parliament could debate bills to incorporate the new territories as soon as Thursday. State-run RIA Novosti said Putin could address parliament on Friday.
Russia says the referendums, hastily organised after Ukraine recaptured territory in a counteroffensive this month, enable people in those regions to express their view.
Luhansk's regional governor said Russian-backed officials were going door to door with ballot boxes and if residents failed to vote correctly their names were taken down.
"A woman walks down the street with what looks like a karaoke microphone telling everyone to take part in the referendum," Luhansk governor Serhiy Gaidai said in an interview posted online.
"Representatives of the occupation forces are going from apartment to apartment with ballot boxes. This is a secret ballot, right?"
The territory controlled by Russian forces in the four regions represents about 15% of Ukraine, of roughly the size of Portugal. It would add to Crimea, an area nearly the size of Belgium that Russia claims to have annexed in 2014.
Ukrainian forces still control some territory in each region, including about 40% of Donetsk and Zaporizhzhia's provincial capital. Heavy fighting continued along the entire front, especially in northern Donetsk and in Kherson.
President Volodymyr Zelenskiy, who insists that Ukraine will regain all its territory, said on Sunday some of the clashes had yielded "positive results" for Kyiv.
"This is the Donetsk region, this is our Kharkiv region. This is the Kherson region, and also the Mykolaiv and Zaporizhzhia regions," he said in nightly video remarks.
In a statement on Facebook, the general staff of the Ukrainian armed forces said Russia had launched four missile and seven air strikes and 24 instances of shelling on targets in Ukraine in the past 24 hours, hitting dozens of towns, including some in and around the Donetsk and Kherson regions.
Reuters could not independently verify the accounts.
PROTESTS IN RUSSIA OVER DRAFT
On Wednesday, Putin ordered Russia's first military mobilization since World War Two. The move triggered protests across Russia and sent many men of military age fleeing.
Two of Russia's most senior lawmakers tackled on Sunday a string of mobilisation complaints, ordering regional officials to swiftly solve "excesses" stoking public anger.
More than 2,000 people have been detained across Russia for draft protests, says independent monitoring group OVD-Info. In Russia, where criticism of the conflict is banned, the demonstrations are among the first signs of discontent since the war began.
In the Muslim-majority southern Russian region of Dagestan, police clashed with protesters, with at least 100 people detained.
Zelenskiy acknowledged the protests in his video address.
"Keep on fighting so that your children will not be sent to their deaths - all those that can be drafted by this criminal Russian mobilisation," he said.
"Because if you come to take away the lives of our children - and I am saying this as a father - we will not let you get away alive."
(Reporting by Reuters bureaus; Writing by Patricia Zengerle and Michael Perry; Editing by Alistair Bell and Clarence Fernandez)