The number of refugees fleeing Ukraine since the Russian invasion launched by President Vladimir Putin on February 24 is now nearly 2.7 million, the UN said on Sunday.

The UN High Commissioner for Refugees said there were 2,698,280 refugees who had fled Ukraine so far, according to its dedicated webpage at around 1100 GMT.

The figure was more than 100,700 higher than the last count on Saturday.

This is the largest exodus of refugees in Europe since World War II, according to UN refugee agency chief Filippo Grandi.

Four million people could leave Ukraine to flee the war, according to initial UN estimates. That figure is likely to be revised upwards, the UN refugee agency said.

Before the conflict, Ukraine had a population of some 37 million in the regions under government control, excluding Russia-annexed Crimea and the pro-Russian separatist regions in the east.

Poland is hosting over half the Ukrainian refugees, with 1,655,503 crossing into the country since the invasion, according to the UNHCR.

For their part, Polish border guards said on Sunday they had registered 1,675,000 people arriving from Ukraine since the war began.

Tens of thousands of people are also entering Ukraine from Poland -- mostly people returning to fight but also others seeking to care for elderly relatives or returning to bring their families to Poland.

Before the crisis, around 1.5 million Ukrainians lived in Poland, the vast majority working in the EU nation.

Hungary had taken in 246,206 refugees by March 12, according to the UNHCR -- around than 10,000 more than it was hosting the previous day.

The UN has said this is the largest exodus of refugees in Europe since World War II
The UN has said this is the largest exodus of refugees in Europe since World War II AFP / GIL COHEN-MAGEN

It has five border posts with Ukraine and several frontier towns, including Zahony, where local authorities have turned public buildings into emergency centres for the refugees.

A total of 195,980 have entered Slovakia from Ukraine, according to the UNHCR, again around 10,000 more than on the previous day.

As of March 10, 106,000 people from Ukraine had sought shelter in Russia.

The UN refugee agency said 96,000 people had crossed into Russia from the pro-Russian Donetsk and Lugansk regions of eastern Ukraine between February 18 and 23.

Many Ukrainians fleeing their country transit through Moldova, a small nation of 2.6 million people and one of the poorest in Europe, to continue onwards to Romania or Hungary.

The UNHCR says 104,929 refugee arrivals were recorded as of Thursday.

Moldovan authorities say that since the start of the war, 284,436 people have entered the country from Ukraine and 185,362 have continued onwards.

The UNHCR has not updated its statistics for Romania but almost 85,000 refugees had been recorded in the country as of March 8. Many refugees travel on to other nations from Romania.

Romanian authorities said 397,542 people had entered the country since February 24, including 16,676 from Ukraine on Saturday alone.

The UNHCR said that as of March 11, about 304,000 people leaving Ukraine had travelled on to other European countries.