Nearly five million Ukrainians have fled the war since Russia's invasion, the United Nations said Tuesday, sounding alarm at the rapid exodus and voicing concern that the situation may worsen.

UNHCR, the UN refugee agency, said 4,980,589 Ukrainians had left since Russia invaded on February 24 -- a figure up 46,174 on Monday'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 around 5.2 million people in all have fled Ukraine since the war began.

Officials call it the fastest-growing refugee crisis in Europe since World War II.

"The key is that the borders remain open, people can access safety and when they get to the neighbouring countries they have access to assistance," UNHCR spokeswoman Shabia Mantoo told reporters in Geneva.

On Tuesday, Russia's defence minister said Moscow was seeking to "liberate" east Ukraine and the ministry said Moscow launched dozens of air strikes across eastern Ukraine overnight. 

Kyiv accuses Russian forces of unleashing a major new offensive in the Donbas region.

"We're watching with concern to see what will happen but it's quite alarming that within the space of a few weeks, we are approaching five million refugees from Ukraine," said Mantoo.

Women and children account for 90 percent of those who fled, 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.

More than 2.8 million Ukrainian refugees have fled to Poland. Three quarters of a million have reached Romania.

UNHCR figures show nearly 645,000 Ukrainians fled in February, with nearly 3.4 million doing so in March and 945,000 leaving so far this month.

Beyond the refugees, the IOM estimates 7.1 million people are displaced within 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 -- 2,800,713 so far -- have crossed into Poland.

Many of them have travelled on to other states in Europe's Schengen open-borders zone.

Meanwhile 738,000 people have crossed from Poland into Ukraine, Polish border guards said.

Before the war, Poland was home to around 1.5 million Ukrainians, chiefly migrant workers.

- Romania -

A total of 750,693 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 535,842 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 465,598 Ukrainians have entered Hungary.

- Moldova -

The Moldovan border is the closest to the major port city of Odessa. A total of 425,227 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.

- Slovakia -

A total of 339,680 people crossed Ukraine's shortest border into Slovakia.

- Belarus -

Another 23,609 refugees have made it north to Russia's close ally Belarus.