"In just seven days, one million people have fled Ukraine, uprooted by this senseless war," UN refugee chief Filippo Grandi said in a statement Thursday.

"Unless there is an immediate end to the conflict, millions more are likely to be forced to flee Ukraine."

The UN Refugee Agency (UNHCR) has projected that more than four million Ukrainian refugees may eventually need protection and assistance, while the European Union's crisis management commissioner has said the figure could reach seven million.

More than 37 million people lived under the Kyiv government's control before last week's invasion.

Here is a breakdown of where the 1,038,583 refugees tallied so far by UNHCR have headed to:

Poland

Just over half of those who have fled Ukraine have crossed west into Poland.

The UNHCR said that 547,982 people had done so. Most arrivals are women and children from all parts of Ukraine.

Polish border officials meanwhile put the number higher, saying Thursday morning that 575,100 people had crossed from Ukraine since the Russian assault began on February 24.

A woman holds her dog as she stands with other displaced Ukrainians on the train platform after arriving from Ukraine at the station in Przemysl, Poland, Thursday, March 3, 2022. AP

They said 95,000 people entered from Ukraine on Wednesday, after 98,000 crossed over on Tuesday.

And the influx continued Thursday, with 27,100 crossing into Poland by 0600 GMT.

Before the current crisis, Poland was already home to around 1.5 million Ukrainians.

Hungary

Some 133,009 people have so far crossed from Ukraine into Hungary, or nearly 13 percent of the total, the agency said.

The country counts five border crossings with Ukraine, and several border towns such as Zahony have turned public buildings into reception centres, with ordinary people donating food and clothes, the interior ministry said.

Thousands of refugees have arrived in Budapest. An AFP photographer saw dozens of refugees disembarking from trains arriving every 30 minutes in the Hungarian capital from the Ukrainian border on Tuesday.

Refugees from Ukraine arrive at the Nyugati Railway Station in Budapest, Hungary, Thursday, March 3, 2022. AP

Moldova

UNHCR said 97,827 people who fled Ukraine were now in Moldova, marking a jump of nearly 20,000 since the last count on Wednesday.

People fleeing the conflict in Ukraine alk after crossing the Moldova-Ukraine border checkpoint near the town of Palanca, on March 2, 2022. AFP

Slovakia

The UNHCR said 72,200 had fled across Ukraine's shortest border to Slovakia, making up seven percent of the total number.

An Ukrainian woman pushes a stroller between shelter tents after crossing the Slovak-Ukrainian border in Vysne Nemecke, Slovakia, on March 2, 2022. AFP

Romania

The UN Refugee Agency said nearly five percent of those who had fled Ukraine, 51,261 people, were now in Romania.

Some refugees reported they had headed to Romania to avoid massive jams at the Polish border.

Most are passing through Siret in the north of the country, where a camp has been set up, along with a second near Sighetu Marmatiei, where volunteers were handing out hot tea, coffee and pizza, as well as flowers and little charms to mark the start of spring, celebrated on Tuesday across the country.

Refugees coming from Ukraine walk at the Ukrainian-Romanian border in Siret on March 02, 2022. AFP

Officials said tens of thousands of refugees who entered Romania have now moved on elsewhere.

Russia

The UNHCR said 47,800 people had fled across Ukraine's longest border since the invasion began -- nearly five percent of the total number.

Belarus

Some 357 people had crossed north from Ukraine into Belarus, the UNHCR said.

Onward Movement

The refugee agency said 8.5 percent of those who had fled Ukraine into neighbouring countries, 88,147 people, had already moved on towards other European states.

Czech Prime Minister Petr Fiala said Wednesday his country had welcomed around 20,000 Ukrainian refugees since the conflict started.

Ukrainian refugees queue to file for residency permits at Prague's foreigner police headquarters on March 2, 2022 in Prague, Czech Republic. AFP

Internally Displaced

Karolina Lindholm Billing, the UNHCR representative to Ukraine, estimated Tuesday that a million people had been internally displaced by the invasion.

She cautioned that the agency still did not have reliable figures.