UNHCR figures show the largest numbers of Ukrainian refugees in non-neighbouring countries were in Germany, the Czech Republic and Italy.
The United Nations has said that, of the more than 6.6 million Ukrainian refugees who have fled to neighbouring countries, 2.9 million have moved on to other European nations.
The figure from the UN refugee agency UNHCR on Friday gave a picture of how many have stayed in the first country they entered and how many have headed on elsewhere as the displacement crisis triggered by the war spreads across the continent.
"According to the latest data we have available... 2.9 million refugees have moved beyond countries neighbouring Ukraine," UNHCR spokeswoman Shabia Mantoo told a briefing in Geneva.
A UNHCR graphic showed the largest numbers of Ukrainian refugees in non-neighbouring countries were in Germany, the Czech Republic and Italy.
A total of 6,659,220 Ukrainians have fled the country since the attack, the agency's figures show. Of those, more than 3.5 million have headed west into Poland.
Around 100,000 refugees per day were arriving at the Polish border in early March but the number has slowed to around 20,000 throughout May.
The first weeks of the war saw volunteers flocking to help either at the borders or in welcoming new arrivals into their homes.
UNHCR spokeswoman Olga Sarrado said strong support from the wider international community would be needed to maintain that generosity and strength of response.
"The needs are only increasing as the conflict" grinds on, she said.
"Support will need to be provided so they can stay in the country until they can go back and live with dignity."
More than 1.1 million people have registered with the Polish authorities and received a state identity number which allows them access to public services.
Some 94 percent of those registered are women and children.
Ukrainians have crossed into Poland more than 2.1 million times since February 28 – though these are not necessarily permanent returns.
"We have also seen more 'pendular' movements, where people go back and forth across the border to Ukraine for various reasons, including visiting families, checking their properties or returning to their jobs," said Sarrado.
"However, Poland expects to continue receiving and hosting a considerable number of refugees, given the large internal displacement, massive destruction and the ongoing hostilities in Ukraine."
READ MORE: UN: More than 100M people forcibly displaced