Moscow began its mandatory troop call-up Thursday to try to bolster a stumbling war effort in Ukraine, with authorities saying thousands had volunteered even as Russian men fled the country to avoid being forced to fight.

Amateur footage posted on social media since President Vladimir Putin ordered the mobilisation of reservists on Wednesday purported to show hundreds of Russian citizens across the country responding to military summons.

The call-up came as Moscow-held regions of Ukraine are to vote in coming days on whether to become part of Russia in referendums that have been called an unlawful land grab by Kyiv and its allies.

Moscow took these steps after Ukrainian forces seized back most of the northeastern Kharkiv region, which has been seen as a possible turning point in the seven-month war that had fallen into stalemate.

The Russian military said Thursday that at least 10,000 people had volunteered to fight in 24 hours since the order, but men also rushed to leave Russia before they were made to join.

Flights out of Russia to neighbouring countries, mainly former Soviet republics that allow Russians visa-free entry, are nearly entirely booked and prices have skyrocketed, pointing to an exodus of Russians wanting to avoid going to war.

"I don't want to go to the war," a man named Dmitri, who had flown to Armenia with just one small bag, told AFP. "I don't want to die in this senseless war. This is a fratricidal war."

Military-aged men made up the majority of those arriving off the latest flight from Moscow at Yerevan airport and many were reluctant to speak.

The Armenian capital has become a major destination for Russians fleeing since war began on February 24, drawing fierce international opposition that has aimed to isolate Russia.

Looking lost and exhausted in Yerevan airport's arrivals hall, 44-year-old Sergei said he had fled Russia to escape being called up.

"The situation in Russia would make anyone want to leave," he told AFP.

Ukrainian President Volodymyr Zelensky called on Russians to resist Putin's partial mobilisation during his daily address on Thursday evening.

"Protest. Fight back. Run away. Or surrender" to the Ukrainian army, he said. "You are already complicit in all these crimes, murders and torture of Ukrainians. Because you were silent. Because you are silent."

More than 1,300 people were arrested during anti-mobilisation demonstrations across Russia on Wednesday, a monitoring group reported.

- Annexation 'vote' -

US Secretary of State Antony Blinken on Thursday demanded Putin be held to account as he faced Russia in a Security Council session in which the United Nations catalogued abuses in Ukraine.

"We cannot -- we will not -- let President Putin get away with it," Blinken said.

Russian Foreign Minister Sergei Lavrov -- whom Blinken has refused to meet individually since the February invasion -- lashed out at Western accusations.

"There's an attempt today to impose on us a completely different narrative about Russian aggression as the origin of this tragedy," Lavrov told the Security Council.

The confrontation on the diplomatic stage escalated as Kremlin-installed officials in Ukrainian regions controlled by Moscow's forces vowed on Thursday to press ahead with annexation polls this week.

Four Russian-occupied regions of Ukraine -- Donetsk and Lugansk in the east and Kherson and Zaporizhzhia in the south -- announced that they would hold the votes over five days, beginning on Friday.

Western leaders convening in New York this week unanimously condemned the ballots.

Speaking at the United Nations, US President Joe Biden accused Russian counterpart Vladimir Putin of "shamelessly" violating the UN Charter with a war aimed at "extinguishing Ukraine's right to exist as a state".

- Nuclear threat -

The integration of the war-scarred regions into Russia would represent a major escalation of the conflict, as Moscow could then try to say it was defending its own territory from Ukrainian forces.

After the votes were announced by his proxy officials in Ukraine, Putin announced that Russia would call up some 300,000 reservists to bolster the war effort and cautioned that Moscow would use "all means" to protect its territory.

Former Russian leader Dmitry Medvedev said in a statement on social media that those means included "strategic nuclear weapons". He predicted the voting regions "will integrate into Russia".

For most observers, the results of the concurrent votes are already a foregone conclusion and were rushed because Ukrainian forces were making sweeping gains in a counter-offensive to recapture the east.

The referendums are reminiscent of a similar ballot in 2014 that saw the Crimean Peninsula in Ukraine annexed by Russia. Western capitals said the vote was fraudulent and hit Moscow with sanctions in response.

Election officials in the Donetsk region, partially controlled since 2014 by Moscow-backed separatists, said voting would take place door-to-door for the first days. But it would only be possible in polling stations on the final day, Tuesday.

Zelensky calls on Russians to 'protest' mobilisation

Ukrainian President Volodymyr Zelensky on Thursday called on Russians to resist the partial mobilisation announced by President Vladimir Putin, which has sparked protests and a fresh exodus out of the country.

"55,000 Russian soldiers died in these six months of war...," Zelensky said in his daily address.

"Want more? No? Then protest. Fight back. Run away. Or surrender" to the Ukrainian army.

"You are already complicit in all these crimes, murders and torture of Ukrainians. Because you were silent. Because you are silent," Zelensky added.

"And now it's time for you to choose: for men in Russia, this is a choice to die or live, to become a cripple or to preserve health.

"For women in Russia, the choice is to lose their husbands, sons, grandchildren forever, or still try to protect them from death, from war, from one person (Putin)," Zelensky continued.

More than 1,300 people were arrested at demonstrations across Russia on Wednesday after the announcement of a partial mobilisation.

There were also reports of a mass exodus following the announcement. Flights out of Russia to the neighbouring countries that allow Russians visa-free entry were nearly entirely booked, while prices skyrocketed.

On Thursday the Kremlin dismissed as "fake" reports that Russians eligible for mobilisation were rushing for the exit.