Flights have sold out and queues have emerged along Russia’s border as Vladimir Putin’s military call-up sparks an exodus.
Prices for air tickets from Moscow soared above $7500 for one-way flights to the nearest foreign locations, with most sold out for coming days.
Traffic also surged at border crossings with Finland and Georgia.
It comes as Russia has begun the mobilisation of up to 300,000 citizens – its biggest conscription since World War II, sparking nationwide protests and a rush on airports.
The Russian government said reports of a mass exodus were exaggerated.
A human rights group says security forces have detained more than 1300 people protesting the war.
At the same time, a top White House Official is quoted as saying the US is taking Russia’s veiled threats to use nuclear weapons seriously.
Russian President Vladimir Putin warned his country would use all the means at its disposal to protect its territory.
US National Security Council Spokesman John Kirby told the BBC the US was not changing its “strategic deterrent posture”, but that Mr Putin spoke irresponsibly.
“It is a dangerous precedent for Mr Putin to be using this kind of rhetoric in the context of a war clearly that he’s losing inside Ukraine,” Mr Kirby told the BBC.
“We have to take these threats seriously and we do … We’ve been monitoring, as best we can, his nuclear capabilities, I can tell you that we don’t see any indication that we need to change our strategic deterrent posture at this point.”
In a further development, former Russian President Dmitry Medvedev has repeated the nuclear threat.
He says any weapons in Moscow’s arsenal, including strategic nuclear weapons, could be used to defend territories incorporated into Russia from Ukraine.
Mr Medvedev, deputy chairman of Russia’s Security Council, said that referendums being organised by Russian-installed and separatist authorities in large swathes of Russian-occupied Ukrainian territory will take place, and that “there is no going back”:
“The Donbas (Donetsk and Luhansk) republics and other territories will be accepted into Russia.”
Mr Medvedev said the protection of all the territories would be significantly strengthened by the Russian armed forces.
“Russia has announced that not only mobilisation capabilities, but also any Russian weapons, including strategic nuclear weapons and weapons based on new principles, could be used for such protection,” he said.
The referendums due to take place in the Russian-held parts of Ukraine’s Donetsk, Luhansk, Kherson and Zaporizhzhia provinces, as well as part of Mykolaiv province, from Friday are widely expected to produce results overwhelmingly endorsing joining Russia.
The votes, being organised at a few days’ notice under military occupation, have been labelled shams by Kyiv and its Western allies.
If formally admitted to the Russian Federation, the occupied territories, where Ukrainian counteroffensives have gathered pace in recent weeks, will under Moscow’s nuclear doctrine be entitled to protection from Russian nuclear weapons.
Moscow does not fully control any of the four regions it is expected to try to annex, with only around 60 per cent of Donetsk and 66 per cent of Zaporizhzhia regions held by the Russian army.
Mr Medvedev has regularly issued aggressive statements on the West and Ukraine in recent months, underlining his transformation from apparently Western-minded liberaliser as president from 2008-2012 to strident geopolitical hawk.
Zelensky calls for Russia to be stripped of its UN veto
Ukraine has urged the United Nations to create a special tribunal and strip Moscow of its UN Security Council veto power.
“A crime has been committed against Ukraine, and we demand just punishment,” President Volodymyr Zelensky, dressed in his trademark green military T-shirt, told world leaders by video at the annual UN General Assembly.
The Security Council has been unable to take significant action on Ukraine because Russia is a permanent veto-wielding member, along with the United States, France, Britain and China.
Meanwhile, a Kyiv government official is quoted as saying Russia’s invasion of Ukraine has caused almost $1 trillion of damage.
-with AAP