The UN estimates the number of people fleeing into neighouring countries could soon hit 4 million if a peace deal is not reached.
A total of 2 million people have now fled Ukrainian territory, the UN refugee agency UNCHR revealed on Tuesday.
Figures collated from officials at border crossing points also reveal which countries the victims of Vladimir Putin’s invasion initially escaped to.
More than half, or 1.2 million, have entered Poland, whose long border is the quickest safe haven to reach from many of Ukraine’s northern and western cities.
While Kyiv, Chernihiv and Kharkiv, early targets for Russian bombing, are closer to Belarus, the country has been used as a staging ground for Russian forces.
Just 453 Ukrainians are estimated to have fled into the dictatorship of Aleksandr Lukashenko, Putin’s sole ally in the invasion.
As the home of Europe’s largest Ukrainian diaspora, Poland is also the first port of call for many Ukrainian refugees hoping to reach expatriated friends and relatives.
Hungary has welcomed the next biggest number of refugees, with 191,348 people crossing the south-western border, followed by Slovakia with 140,745.
Moldova, home to Europe’s second-largest population of Ukrainian expats, has reported 82,762 crossings, while Romania has had 82,062.
Just over 99,000 people moved to Russia from the separatist-controlled Ukrainian regions of Donetsk and Luhansk in the week before the invasion, the UNHCR added.
It is not known how many more have entered Russian territory since then, as the Kremlin refuses to share data.
Some 210,000 are estimated to have made it to other European countries such as the UK, where Boris Johnson is under mounting pressure from charities and his own ministers to speed up the visa process for refugees.
British visas have been granted to 300 Ukrainians under a new scheme so far, according to the Home Office, while another 17,700 applications to join previously settled relatives have yet to be fully processed.
As the UNHCR released the figures, the agency’s chief, Filippo Grandi, tweeted in recognition of March 8’s International Women’s Day: ‘Men cause futile and cruel wars to prove that they are strong.
‘But it is on the real strength of women that societies must count to remain resilient and to build peace.’
His officials warned that the number of refugees is expected to hit 4 million, nearly one-tenth of the country’s population.
Millions more are believed to be internally displaced as Russian shelling forced entire cities to evacuate their citizens, many of whom are travelling on foot or crammed into minibuses taking them to crowded makeshift shelters.
Since Russia’s invasion of Ukraine began on February 24, the country has suffered widespread damages and loss of life amid a major bombing campaign.
An estimated 1.5 million refugees have fled Ukraine, as cities face shortages of food, water, heat, and medicine.
Countries have retaliated by imposing sanctions on Russia, with individual companies boycotting Russian products.
This has led to Russian President Vladimir Putin publishing a list of 43 ‘unfriendly countries’ who face economic restrictions for their sanctions.
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