UNHCR, the UN refugee agency, said 3,169,897 Ukrainians had fled across the border since the war began on February 24, a figure up 106,802 since Wednesday's update.

"More than three million people have fled the country, the vast majority women, children and older people who left behind their homes and often family members, not knowing what's to come," the agency said.

"Hour by hour, minute by minute, people are fleeing the terrifying reality of violence in Ukraine. Unless the conflict ends, this heart-breaking crisis is set to grow. We need peace, now."

The UNHCR said that more than two million people still within Ukraine's borders had also fled their homes.

The UN's International Organization for Migration said 162,000 third-country nationals had fled the country, as of Wednesday.

The UNHCR initially estimated that up to four million people could leave Ukraine, but last week admitted 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 the UNHCR:

Poland

Six in 10 Ukrainian refugees crossed the Polish border, or some 1,916,445 people so far.

The Polish border guards said incoming numbers were down 11 percent on Wednesday compared to Tuesday.

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 returning to bring their families out to Poland.

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

The data of arrivals into Ukraine's neighbouring countries which are in Europe's Schengen open-borders zone -- Poland, Hungary and Slovakia -- only represent border crossings into that country.

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

Romania 

The UNHCR said 491,409 people had made their way into neighbouring Romania, including people who had crossed over from Moldova to reach the EU member state.

The UNHCR figures per neighbouring country are 271,283 higher than their overall total -- a difference which the agency says reflects the number of people who crossed between Moldova and Romania.

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

Moldova 

The UNHCR said 350,886 Ukrainians had crossed into the non-EU state. 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 

A total of 282,611 Ukrainian refugees crossed into Hungary.

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

Some 228,844 refugees made it across Ukraine's shortest border into Slovakia.

Russia

Some 168,858 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 February 21 and 23.

Belarus

Some 2,127 refugees have made it to Belarus, the UNHCR says.