"The current total is now 368,000 and continues to rise," United Nations High Commission for Refugees or UNHCR said in a tweet, adding the new figure was based on "data made available by national authorities".
A large number of those escaping to neighbouring countries have crossed over into Poland, where the authorities have counted some 156,000 crossing since the invasion started early Thursday.
Border guards counted some 77,300 arrivals from Ukraine on Saturday alone.
The refugees have arrived in cars, in packed trains and even on foot.
Those who arrive with nowhere to go can count on the help of volunteers -- both members of NGOs and private citizens.
Others have also headed to Moldavia, Hungary, Slovakia and Romania.
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