The UN Refugee Agency's chief Filippo Grandi blamed the mass displacement on what he called a "senseless war" that began on Feb 24 when Russian troops invaded.

"The number of refugees from Ukraine, tragically, has reached today 2.5 million," Grandi tweeted.

"We also estimate that about two million people are displaced inside Ukraine. Millions forced to leave their homes by this senseless war."

Paul Dillon, spokesman for the UN's International Organization for Migration, said the 2.5 million people who had fled Ukraine included 116,000 nationals from other countries.

The UNHCR had been working on the estimate that four million people may eventually seek to leave Ukraine as the war continues.

But the agency said that given the scale of the exodus in less than three weeks, it would be no surprise if that figure was exceeded.

"It is quite possible that that planning figure of four million might be revised up," UNHCR spokesman Matthew Saltmarsh told reporters in Geneva, speaking via videolink from Poland, close to the Ukrainian border.

He said the numbers of refugees was "certainly unprecedented since World War II".

Before Russia invaded, more than 37 million people lived in Ukrainian territory under the control of the central government in Kyiv.

More than half of those who have fled have gone to Poland.

Poland's border guards announced Friday that 1.52 million people fleeing Ukraine had crossed the frontier, with a further 87,000 people doing so on Thursday.

Poland has championed the cause of Ukrainian refugees. The government has set up reception centres and charities have mobilised in a massive aid effort, helped by the estimated 1.5 million Ukrainians already living in the EU member state.

Polish border guards said Thursday that 140,000 people had crossed from Poland into Ukraine since the invasion.

They largely fall into three categories: Ukrainian men working in Poland who returned to join the army, migrant workers returning to take care of relatives still in Ukraine, and recently-arrived refugees who have gone back for family reasons.

Several thousand refugees, once they have crossed Ukraine's western borders, have headed on to other countries.

Russian strikes hit civilian targets in central Ukraine's Dnipro city on Friday, as Moscow's troops edged closer to the capital Kyiv that, according to its Mayor Vitali Klitschko, has lost half of its estimated 3.5 million population since the war began.

"UNHCR repeats its call for the protection of civilians and civilian infrastructure," Saltmarsh said.

"We are committed to stay and deliver assistance when and where access and security allow."