GENEVA (AFP) - More than 3.3 million refugees have now fled Ukraine since the Russian invasion, the United Nations said on Saturday (March 19), while nearly 6.5 million are thought to be internally displaced within the country.

UNHCR, the UN refugee agency, said 3,328,692 Ukrainians had left since the war began on Feb 24, with another 58,030 joining the exodus since Friday's update.

"People continue to flee because they are afraid of bombs, air strikes and indiscriminate destruction," said UNHCR chief Filippo Grandi.

"Aid is vital but can't stop fear. Only stopping the war can."

About 90 per cent of those who have fled are women and children. Ukrainian men aged 18 to 60 are eligible for military call-up and cannot leave.

The UN's International Organisation for Migration (IOM) also said that as of Wednesday, 162,000 third-country nationals had fled Ukraine.

Millions more have fled their homes but remain within Ukraine's borders.

Some 6.48 million people were estimated to be internally displaced within Ukraine as at Wednesday, following an IOM study.

UNHCR initially estimated that up to four million people could leave Ukraine, but last week said that figure might well be revised upwards.

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

Here is a breakdown of where Ukrainian refugees headed to, according to UNHCR:

Poland

Six in every 10 Ukrainian refugees - or 2,010,693 people so far - have crossed the Polish border, according to the UNHCR's latest figures.

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

But many of those arriving from Ukraine in neighbouring Poland, Hungary and Slovakia are then travelling further on into other nations of Europe's Schengen open-borders zone.

"We estimate that a large number of people have moved onwards to other countries," UNHCR said.

Romania

The UNHCR said more than half a million Ukrainians had now made their way into Romania.

Some 518,269 have reached the country, including people who had crossed over from Moldova to reach the EU member state.

The vast majority are thought to have made their way to other countries farther into Europe.

Moldova

The UNHCR said 359,056 Ukrainians had crossed into the non-EU state wedged between Romania and Ukraine. It is the closest border to the major port city of Odessa.

Many Ukrainians fleeing the fighting transit through Moldova, a small nation of 2.6 million people and one of the poorest in Europe, en route westwards to Romania and other countries beyond.

Hungary

Ukrainian refugees who have crossed into Hungary number 299,273.

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

Slovakia

A total of 240,009 Ukrainians made it across the country's shortest border into Slovakia.

Russia

Some 184,563 refugees have sought shelter in Russia.

In addition, UNHCR said 50,000 people had crossed into Russia from the pro-Russian Donetsk and Lugansk regions of eastern Ukraine between Feb 21 and 23.

Belarus

The UNHCR says 2,548 refugees have made it to Belarus.