The Foreign Office is advising all British nationals currently in Georgia to leave as soon as possible unless they have an urgent need to stay.
Officials earlier advised against all non-essential travel to the conflict-hit country, but stepped up their warning following further fighting.
Violence has erupted between Russian and Georgian forces over control of the breakaway South Ossetia region.
Foreign Secretary David Miliband has called for an immediate ceasefire.
Air services
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He said then that there was "no immediate cause for alarm" and British nationals were not being advised to leave the country.
However, on Sunday, the Foreign Office issued new advice.
It said in a statement: "If you or your family have no urgent need to remain in Georgia you should leave as soon as possible.
"It is wise to do so while some air services are still available and the border remains open."
The Foreign Office is also advising against all travel to the separatist regions of South Ossetia, Abkhazia and the upper Kodori.
It said serious fighting was continuing in South Ossetia and there had been aerial bombardment of Georgian military installations outside the conflict zone at the Black Sea port of Poti and the military bases at Vaziani, Senaki and Marneuli.
Mr Miliband has said the government is "deeply concerned" by the violence in Georgia.
He has held talks with European foreign ministers and with US Secretary of State Condoleezza Rice over how to respond to the crisis.
Based on Russian and South Ossetian estimates, the death toll on the South Ossetian side is believed to be at least 1,500, mostly civilians. Georgian casualty figures range from 82 dead, including 37 civilians, to a figure of about 130 dead.
(BBC)
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