One-way flights out of Russia have reportedly started selling out after Vladimir Putin ordered the immediate call-up of 300,000 reservists.
On Monday, the Russian president announced the partial mobilisation of the country's military reserves following a humiliating defeat in Kharkiv.
In a chilling threat, he added Moscow would respond with the might of its vast arsenal if the West pursued what he called its "nuclear blackmail" over the conflict, adding: "I'm not bluffing."
Putin added: "If there is a threat to the territorial integrity of our country and for protecting our people, we will certainly use all the means available to us."
The mobilisation is Russia's first since the Second World War and signifies a major escalation of the conflict, which is now in its seventh month.
However, the early-morning television address appears to have led many Russians to see to flee the country.
The Russian government has yet to announce which citizens will be exempted, though defence minister Sergei Shoigu said the call-up would be limited to those with experience as professional soldiers, and that students and those who had only served as conscripts would not be called up.
Watch: Former advisor to Vladimir Putin says West will be to blame for nuclear war in BBC rant
Nevertheless, according to the Reuters news agency, Google Trends data showed a spike in searches for Aviasales, which is Russia's most popular website for purchasing flights.
Other analysts have reported other flights already being sold out.
RTE Europe editor Tony Connelly tweeted: "All tickets for flights to Yerevan, Armenia and Istanbul, Turkey as well as to Tbilisi, Georgia from Russia reportedly sold out shortly after speech given by President Putin."
Tickets to Azerbaijan Kazakhstan, Uzbekistan and Kyrgyzstan have also been selling fast, according to Aviasales.
New York Times correspondent Valerie Hopkins added: "Direct flights from Moscow to Istanbul & Yerevan, which allow Russians visa free entry, were sold out on Weds.
"Some routes w stopovers, like Moscow-Tbilisi, were also unavailable. Cheapest flights MSK- Dubai were >300K RUB ($5,000) - 5x avg monthly wage."
Maria Antonova, a former journalist for the AFP news agency, tweeted: "Panic in Russia over announced mobilisation (which is not really 'partial' if you read the decree carefully rather than listen to speeches).
"First reports of eligible men turned away from border crossings to Georgia. People are still able to fly out but tickets are sold out."
Despite rumours of border closures circulating social media, Russian Railways and airline Aeroflot denied reports that they had been ordered to ban men aged 18 to 65 from buying tickets.
Latvia, a member of the European Union which borders Russia, will not offer refuge to any Russians fleeing Moscow's mobilisation due to security concerns, the country's foreign minister Edgars Rinkevics said.
Putin was initially due to deliver his televised address to the nation on Tuesday night, but for an unknown reason, postponed it to Wednesday morning.
During this time, Google searches for "how to leave Russia" spiked in the country, as pointed out by Mozhem Obyasnit.
The Telegram channel founded by Russian dissidents said residents in Russia's far eastern territory of Khabarovsk, which borders China, had a particular interest in fleeing.
In a statement on Twitter, Ukraine's defence ministry said: "The Russians were given 12 hours of rest, so Google could answer all the questions, including the question of what is the average life expectancy of a Russian a soldier in Ukraine."
Meanwhile, UK defence secretary Ben Wallace said Putin’s call-to-arms was an "admission that his invasion is failing".
In recent weeks, Ukrainian forces have staged a fierce counter-offensive in south and east of the country, forcing Moscow to concede swathes of territory.
Russian troops left behind valuable military equipment and vehicles as they retreated from the region surrounding the city of Kharkiv, suggesting they were forced to leave in a hurry.
It is unclear whether Russian frontline forces have “sufficient reserves or adequate morale” to withstand another concerted assault in eastern parts of Ukraine, UK defence intelligence analysts said.
They believe Moscow has established a defensive line between the Oskil River and the town of Svatove after being pushed back by Ukraine.
The zone is viewed as important partly because it sits along the border of the Luhansk region, part of the Donbas, which Russia has sought to “liberate” as one of its key war aims.
Any substantial loss of territory here would “unambiguously undermine” Putin’s strategy for the conflict, the experts say.