Shabia Mantoo, spokesperson of the UN High Commissioner for Refugees (UNHCR), said the figures were compiled from reports from national authorities and its staff and partner agencies. "It's a ballpark figure," she told Reuters.
Central European countries across the region are bracing for many more refugees, setting up reception points and sending troops towards the borders to provide assistance.
The countries on the European Union's eastern flank were all once part of the Moscow-led Warsaw Pact and are now members of NATO.
Among them, Poland, Hungary, Slovakia and Romania all share land borders with Ukraine.
Russia has launched an all-out invasion of Ukraine by land, air and sea, the biggest attack by one state against another in Europe since World War Two.
It has fuelled fears of a massive flood of refugees fleeing Ukraine, a nation of 44 million people.
Poland called for the "fiercest possible sanctions" against Russia.
Czech President Milos Zeman, long sympathetic to Moscow, called Russian President Vladimir Putin a "madman" and Prague stopped issuing visas to Russians and ordered closure of two Russian consulates.
Hungary's Prime Minister Viktor Orban, who has also forged good ties with Putin, also condemned Moscow's actions.
He said Hungary would prepare humanitarian aid for Ukraine and was ready to receive refugees.
Ukrainians started trickling into Poland, home to the region's largest Ukrainian community of around one million and the easiest EU country to reach from Kyiv.
Dozens were arriving at the normally quiet Medyka crossing on Thursday, some carrying luggage and accompanied by children.
Groups of people also fled into Hungary via the Beregsurany and Tiszabecs crossings, some coming from as far as Kyiv, a Reuters eyewitness said. Some arrived by car but many pedestrians were also hauling suitcases across.
Slovak customs officials said passenger cars were having to wait up to eight hours at the busiest of Slovakia's three road crossings with Ukraine.
Poland was preparing a medical train to transport wounded Ukrainians and drew up a list of 1230 hospitals that could admit the injured, the health ministry said. The Polish army raised the level of preparedness of some units.
"We will do everything to ensure that every person who enters the territory of Poland has access to healthcare, including hospitalisation," the ministry said.
Germany offered humanitarian help to countries bordering Ukraine. German media have cited estimates that between 200,000 and one million people may flee to the EU from Ukraine.
