TBILISI/HELSINKI - Some Russian men rushed for the exits on Thursday after President Vladimir Putin ordered a partial mobilisation, with traffic at border crossings with Finland and Georgia surging and prices for air tickets from Moscow rocketing.

Putin on Wednesday ordered Russia's first mobilisation since World War Two and backed a plan to annex swathes of Ukraine, warning the West he was not bluffing when he said he'd be ready to use nuclear weapons to defend Russia.

Prices for air tickets out of Moscow soared above $5,000 for one-way tickets to the nearest foreign locations, with most air tickets sold out completely for coming days.

Social media groups popped up with advice on how to get out of Russia while one news site in Russian gave a list of "where to run away right now from Russia." There were long tailbacks at border crossings with Georgia.

"War is horrible," Sergei, a Russian man who declined to give his surname, told Reuters as he arrived in Belgrade, the Serbian capital. "It's okay to be afraid of war and of death and such things."

One Russian man who gave his name as Alex told Reuters in Istanbul that he had left Russia partly due to the mobilisation.

"The partial mobilisation is one of the reasons why I am here," he said. "A very poor step it seems to be, and it can lead to lots of problems to lots of Russians."

He said he felt that not many Russians would want to be sent to fight.

Another Russian, who gave his name only as Vasily, arrived in Istanbul with his wife, teenage daughter and six suitcases.

"The mobilization was inevitable because there was a shortage of human resources. I am not worried because I’m already 59 years old and my son lives abroad," he said.

Kremlin spokesman Dmitry Peskov said on Thursday that reports of an exodus of draft-age men were exaggerated. Asked about reports that men detained at anti-war protests were being given draft papers, Peskov said it was not against the law.

Russian state-owned pollsters say that more than 70% of Russians support what the Kremlin calls the "special military operation", though polling leaked in July showed an even split between those who wanted to fighting to stop or continue.

The war in Ukraine has killed tens of thousands, unleashed an inflationary wave through the global economy and triggered the worst confrontation with the West since the 1962 Cuban Missile Crisis, when many feared nuclear war imminent.

$5,000 TICKETS

A tourism industry source told Reuters that there was desperation as people sought to find air tickets out of Russia.

"This is panic demand from people who are afraid they won't be able to leave the country later - people are buying tickets not caring where they fly to," the source said.

Traffic arriving at Finland's eastern border with Russia "intensified" overnight and remained elevated into daytime hours on Thursday, the Finnish Border Guard said.

"The number clearly has picked up," the Finnish border guard's head of international affairs, Matti Pitkaniitty, told Reuters, adding that the situation was under control and border guards were ready at nine checkpoints.

Traffic from Russia was busier than normal at the Vaalimaa crossing - one of nine with Russia - with three lanes of cars each stretching for 300-400 metres (yards), a border official there told Reuters.

Estonia, Latvia, Lithuania and Poland, the other EU countries that border Russian territory, began turning away Russians from crossings at midnight on Monday, saying they should not travel while their country is at war with Ukraine.

The Russian national airline, Aeroflot, said it would refund people who were unable to fly as planned because they had received a call-up.

Russian police detained more than 1,300 people in Russia on Wednesday at protests denouncing mobilisation, a rights group said.

In the far eastern region of Yakutia, a military commissar ordered a call for mobilisation.

(Additional reporting by Mehmet Emin Caliskan, Bulent Usta, David Gauthier-Villars in Istanbul, Writing by Caleb Davis and Guy Faulconbridge, editing by Mark Heinrich, Frank Jack Daniel, William Maclean)