The number of Ukrainian refugees fleeing Russia's war in their country has crossed 4.1 million, the United Nations said Friday, adding: "This tragedy must stop".

The flow of people escaping across the western borders to flee the Russian assault has settled at around 40,000 a day over the past week.

UNHCR, the UN refugee agency, said 4,102,876 Ukrainians had fled the country since the February 24 invasion -- a figure up 43,771 on Thursday's numbers.

More than 3.4 million fled in March.

"Forced to run for their lives. Forced to leave their homes. Forced to be apart from family. This tragedy must stop," UNHCR said.

Women and children account for 90 percent of those who have fled. Half of those are children. Ukrainian men aged 18 to 60 are eligible for military call-up and cannot leave.

UNICEF, the UN children's agency, says more than half of the country's estimated 7.5 million children have been displaced -- 2.5 million internally and two million abroad.

The UN's International Organization for Migration (IOM) said that in addition to Ukrainian refugees, more than 204,000 non-Ukrainians living, studying or working in the country have also left.

And as of March 16, some 6.48 million people were estimated to be internally displaced within Ukraine, an IOM survey showed.

"Forced to flee extraordinary levels of violence, they have left behind their homes and often their families, leaving them shocked and traumatised," said UNHCR chief Filippo Grandi, wrapping up his first visit to Ukraine since the invasion.

"The protection and humanitarian needs are enormous, and continue to grow. And while critically urgent, humanitarian aid alone cannot give them what they really need -- and that is peace."

He added: "The support and solidarity shown so far by donors, neighbouring countries, and private individuals from around the world has been remarkable."

Before the Russian invasion five weeks ago, 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 how many Ukrainian refugees have fled to neighbouring countries, according to UNHCR:

- Poland -

Nearly six out of 10 Ukrainian refugees -- 2,384,814 so far -- have crossed into Poland. 

More than 1.1 million children have arrived in Poland, said UNICEF.

Many people who cross into Ukraine's immediate western neighbours travel onto other states in Europe's Schengen open-borders zone.

- Romania -

A total of 623,627 Ukrainians have entered the EU member state, including a large number who crossed over from Moldova, wedged between Romania and Ukraine. 

The vast majority are thought to have gone on to other countries. 

- Moldova -

The Moldovan border is the closest to the major port city of Odessa. Some 390,187 Ukrainians have crossed into the non-EU state, one of the poorest in Europe.

The UN's World Food Programme has started cash assistance for 100,000 refugees and their host families in the country.

- Hungary -

A total of 374,535 Ukrainians have entered Hungary. 

- Russia -

Some 350,632 refugees had sought shelter in Russia as of Tuesday.

In addition, 113,000 people crossed into Russia from the separatist-held pro-Russian regions of Donetsk and Lugansk in eastern Ukraine between February 21 and 23. 

- Slovakia -

A total of 292,039 people have crossed Ukraine's shortest border into Slovakia. Another 2,823 Ukrainians entered Slovakia on Thursday.

- Belarus -

Another 12,746 refugees have made it north to Russia's close ally Belarus.