Tens of thousands of Ukrainians have fled their country since Russia invaded Thursday.
The United Nations’ refugee agency, UNHCR, says it is planning to deal with up to four million if the situation worsens.
But the European Union’s crisis management commissioner says the figure could reach seven million.
Poland
Some 196,000 Ukrainians have already fled over the Polish border, its frontier guards said Sunday. On Friday alone, 50,000 Ukrainians arrived.
While 90 percent of the refugees are being put up by friends or relations, nine reception centres are also being set up close to the frontier.
Poland was already home to 1.5 million Ukrainians before Russia invaded.
Across the country people are mobilising to offer accommodation, money, clothes and work to the new arrivals.
Romania
Of the 47,000 Ukrainians who have crossed into Romania since Thursday, 22,000 have already gone on to other countries, the government says.
Most are passing through Siret in the north of the country, where a camp has been set up with a second near Marmatiei. Romanians have also taken to social media to donate food and clothing to the refugees.
Hungary
Some 71,000 Ukrainian refugees have crossed into Hungary since the invasion, says the country’s interior ministry.
Several border towns such as Zahony have set up public buildings as reception centres, with ordinary people donating food and clothes.
Moldova
At least 70,000 Ukrainians have also crossed into Moldova, the country’s deputy prime minister said.
The UNHRC’s central Europe chief Roland Schilling hailed the small nation for its response to a “heartbreaking situation”.
He said local people as well as the Moldovan government “have been really impressive” in the way they are dealing with the flow.
Prime Minister Natalia Gavrilița visited the border crossing of Palanca Saturday where a tent village and medical facilities have been set up.
“In these dark days for Ukraine, we stand by its citizens,” she tweeted. “Moldova will assist those in need of safe transit or shelter. We are with you Ukraine!”
Slovakia
More than 17,600 Ukrainians have crossed into Slovakia since Thursday, the UNHCR said. The Slovak ministry of interior told AFP that 6,514 crossed on Sunday between midnight and 6 am alone.
Internally displaced
Some 160,000 people are thought to be internally displaced within Ukraine.
“Displacement in Ukraine is growing but the military situation makes it difficult to estimate numbers and provide aid,” United Nations refugee chief Filippo Grandi tweeted Saturday.
But the EU crisis commissioner Janez Lenarcic said Sunday that “we are witnessing what could become the largest humanitarian crisis on our European continent in many, many years,” with up to seven million displaced and 18 (million) “affected in humanitarian terms”.