Poland has received the largest group of refugees, numbering 281,000. The EU is preparing to grant Ukrainians the right to stay and work in the EU for three years.
According to the UN, more than half fled into Poland.
Where are Ukrainian refugees going?
"More than 500,000 refugees have now fled from Ukraine into neighboring countries," UN refugee chief Filippo Grandi said in a tweet.
UN refugee agency spokeswoman Shabia Mantoo said that the current count had 281,000 refugees from Ukraine in Poland, and more than 84,500 in Hungary. More than 36,400 were in Moldova, with 32,500 in Romania and 30,000 in Slovakia, Mantoo said.
The UN agency said that many refugees were moving onward to other European countries, and some 34,600 had already done so.
Meanwhile, a spokesperson for the German interior ministry said that 1,800 refugees from Ukraine had arrived in Germany so far.
EU to grant fleeing Ukrainians right to stay and work
The EU is preparing to allow fleeing Ukrainians the right to stay and work in the 27-nation bloc for up to three years, senior EU and French officials said.
"It is our duty to take in those who flee war," French Interior Minister Gerald Darmanin told France 2 TV on Monday, saying the EU interior minister had on Sunday tasked the European Commission with preparing draft proposals to grant them protection.
Ministers will meet again on Thursday to agree on details. The EU temporary protection directive, drawn up after the 1990s war in the Balkans but so far never used, provides for the same level of protection for one to three years in all EU states. That includes a residence permit, as well as access to employment, social welfare and medical treatment.
Civilians suffer as Ukraine war rages on
As Russia's assault on Ukraine continues, civilians are scrambling to flee the country. Others are holed up in bomb shelters and even subway stations.
Kyiv residents have been improvising with various means to repel Russian forces. Here, members of the civil defense prepare Molotov cocktails.
Image: Efrem Lukatsky/AP Photo/picture alliance
Standing tall
Residents in Kyiv have formed civil defense units to protect their city and their families. Here an armed civil defense guard patrols a street in Kyiv after the curfew.
Image: Efrem Lukatsky/AP Photo/picture alliance
Waiting in fear
Those that are unable to flee the assault on Kyiv take shelter wherever they can find refuge. Many go to underground shelters or subway stations when the air-raid sirens go off.
Image: Kunihiko Miura/AP/picture alliance
Torn apart
Despite Russian assurances not to target civilian buildings, rockets and mortars have landed in residential areas like this apartment building in Kyiv, which was damaged on February 26.
Image: Efrem Lukatsky/AP/dpa/picture alliance
In shock
A woman stands outside her badly damaged home after a rocket attack in Kyiv on Friday, February 25. Russian forces have hit civilian targets in several cities across Ukraine since Thursday.
Image: Emilio Morenatti/AP Photo/picture alliance
Unabated onslaught
During the night from Friday into Saturday morning, Russian attacks on Kyiv continued. This high-rise residential building in the capital was struck by a missile, according to Kyiv Mayor Vitali Klitschko. He urged city residents to stay out of harm's way.
Image: Gleb Garanich/REUTERS
Seeking safety
People shelter in a basement as sirens warn of fresh attacks on Kyiv. Russia launched an all-out attack on Ukraine in the early hours of February 24.
Image: Emilio Morenatti/AP/picture alliance
Subway station turned bomb shelter
Residents of Kyiv have also been taking to metro stations to stay safe as fighting rages on. The city has a population of roughly 3 million people.
Image: Zoya Shu/AP/dpa/picture alliance
Fleeing the war zone
Civilians evacuated by train from eastern Ukraine arrive at Lviv, in the country's west. Neighboring Poland, Hungary, and Romania are receiving scores of refugees.
Ukrainians carrying their belongings at Astely-Beregsurany border crossing, escaping to Hungary. Long queues have formed at the border, as people are desperate to leave.
Image: Janos Kummer/Getty Images
Safe, at last
Two Ukrainian refugees embrace as they arrive in Hungary after passing Beregsurany border crossing on February 26. Hungarian Prime Minister Viktor Orban vowed to provide humanitarian assistance for the new arrivals.
Image: Bernadett Szabo/REUTERS
Volunteers doing what they can
Volunteers prepare sandwiches for Ukrainian refugees fleeing to Romania via Siret border crossing, on Friday, February 25. Romanian authorities have readied for an influx of Ukrainians.
Image: Andreea Alexandru/AP/picture alliance
Not going anywhere
Ukraine's president, Volodymyr Zelenskyy, continues to send out defiant messages to his fellow Ukrainians boosting the morale of Ukrainian fighters as Russian troops
were closing in on the city and huge explosions were heard early on February 27.