GENEVA (AFP) - Refugees now fleeing Russia's invasion of Ukraine are "more traumatised" than those who escaped in the first phase of the war, the UN said on Friday (March 18).

While those who made an early decision to leave were often those with contacts outside the country, a plan in mind and a place to stay, those fleeing Ukraine now are more likely to be lost as to what to do next, the UN Refugee Agency said.

Spokesman Matthew Saltmarsh, in Rzeszow in Poland near the Ukrainian border, said those fleeing now were in greater need of assistance.

"That is certainly something that we've noticed in the last five to six days in Poland," he told reporters in Geneva via video-link.

"Those refugees who have been arriving have been more traumatised. They've been in shock, many of them. I think it's fair to say that they have fewer means than those who arrived in the earliest phase of this crisis."

The UN Refugee Agency, UNHCR, says 3.27 million people have now fled Ukraine since Russia's full-scale invasion began on Feb 24.

Polish border guards say two million have crossed west into their country.

"What we've noticed with many of them is they don't have a plan when they arrive," Saltmarsh said of recent arrivals.

"Many of those in the first phase might have had friends, diaspora networks, contacts and relatives to whom they could go and stay with intially, and then make a plan from there.

"That's been less the case recently, which means that those who arrived are not clear where they can go.

"That in turn has been putting more pressure on the Polish authorities, who have been reaching out to more municipalities and more regions to say 'can you step up and can you find accommodation and places for the new arrivals'."