The UK said the number of fleeing Russians likely exceeded Putin's original invasion force.
Reports said least 190,000 Russians had left since Putin said he would draft reservists for Ukraine.
The exodus is likely to affect Russia's economy and add to "brain drain," the UK said.
The number of Russians leaving the country to avoid President Vladimir Putin's latest mobilization for the war in Ukraine is likely bigger than the original invasion force, UK intelligence said.
The UK's Ministry of Defense tweeted this estimate on Thursday, writing that there had been a "considerable exodus of Russians seeking to evade call-up."
"Whilst exact numbers are unclear, it likely exceeds the size of the total invasion force Russia fielded in February 2022," it said.
—Ministry of Defence 🇬🇧 (@DefenceHQ) September 29, 2022
Since Putin announced on September 21 that he would call up 300,000 reservists, there has been a mass rush for the border as Russians attempt to evade being sent to the front lines.
Putin had pledged in March not to introduce conscription, a move that has helped to keep Russian civilians removed from the realities of the invasion of Ukraine. That was sharply interrupted with last week's announcement.
The Associated Press reported that as of Wednesday, at least 194,000 Russians had fled to Georgia, Kazakhstan and Finland alone.
Those estimates exceed what the US had estimated to be a 190,000-strong invasion force that massed at Ukraine's border just before the invasion.
On Monday, the satellite-imaging company Maxar shared pictures of huge traffic buildups at Russia's borders with Georgia and Mongolia.
Ten thousand people have crossed into Georgia each day since the announcement, double the normal traffic, The Washington Post reported.
The UK's Ministry of Defense said on Thursday: "The better off and well educated are overrepresented amongst those attempting to leave Russia."
Russia's ultrarich were on the move long before this announcement. According to the wealth-intelligence firm New World Wealth, by mid-March, 15,000 Russian millionaires were projected to leave the country.
The situation is likely to compound the country's economic woes and "brain drain" effect, the ministry said.
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