Many of the nearly five million people who have fled Ukraine will not have homes to return to, the United Nations said Saturday as another 40,000 fled the country in 24 hours.

UNHCR, the UN refugee agency, said 4,836,445 million Ukrainians had left the country since the Russian invasion on February 24 -- a number up 40,200 on Friday's total.

The UN's International Organization for Migration (IOM) says nearly 215,000 third-country nationals -- largely students and migrant workers -- have also escaped to neighbouring countries, meaning more than five million people in all have fled Ukraine since the war began.

It is one of the fastest-growing displacement and humanitarian crises ever.

"People's greatest wish is to go back home. But for so many, there is no home to return to since it's been destroyed or damaged, or is located in an area that is not safe," said Karolina Lindholm Billing, UNHCR's representative in Ukraine.

"Housing is one of the areas of greatest concern. Although hundreds of thousands of people are now staying in temporary reception centres or with hosting families who have generously opened their homes... longer term solutions need to be found."

Nearly 2.75 million Ukrainian refugees -- nearly six in 10 -- have fled to Poland. More than 730,000 reached Romania.

UNHCR figures show nearly 645,000 Ukrainians fled in February, with nearly 3.4 million doing so in March and more than 800,000 leaving so far this month.

Women and children account for 90 percent of those who escaped, with men aged 18 to 60 eligible for military call-up and unable to leave.

Nearly two-thirds of all Ukrainian children have been forced from their homes, including those still inside the country.

Beyond the refugees, the IOM estimates 7.1 million people have left their homes but are still in Ukraine.

Before the invasion, Ukraine had a population of 37 million in the regions under government control, excluding Russia-annexed Crimea and the pro-Russian separatist-controlled 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 -- 2,744,778 so far -- have crossed into Poland.

Many people who go to Ukraine's immediate western neighbours travel on to other states in Europe's Schengen open-borders zone.

Magdalena Tosheva, the IOM's site manager at the Medyka crossing in southeastern Poland, said that despite a decrease in arrivals, refugees still needed access to information, transport, accommodation, work and education.

"People were arriving stressed, tired and cold from the other side of the border," she said.

"Vulnerable people are mainly women with very small children with no solutions, no relatives here, no protective environment."

- Romania -

A total of 732,473 Ukrainians 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. 

- Russia -

Another 484,725 refugees have sought shelter in Russia.

In addition, 105,000 people crossed into Russia from the separatist-held pro-Russian regions of Donetsk and Lugansk in eastern Ukraine between February 18 and 23.

- Hungary -

A total of 454,098 Ukrainians have entered Hungary.

- Moldova -

The Moldovan border is the closest to the major port city of Odessa. A total of 421,130 Ukrainians have crossed into the non-EU state, one of the poorest in Europe.

Most of those who have entered the former Soviet republic of 2.6 million people have moved on but an estimated 100,000 remain, including 50,000 children -- of whom only 1,800 are enrolled in schools.

- Slovakia -

A total of 332,707 people crossed Ukraine's shortest border into Slovakia.

- Belarus -

Another 22,827 refugees have made it north to Russia's close ally Belarus.