More than 1.5 million people have fled Ukraine since the start of the Russian invasion, according to the latest UN data on Sunday.

The United Nations High Commissioner for Refugees (UNHCR) had recorded 1,534,792 refugees on its dedicated website by 1335 GMT, almost 166,000 more than the previous count on Saturday.

Authorities and the UN expect the flow to intensify as the Russian army continues to advance into Ukraine, particularly as it approaches the capital, Kyiv.

"More than 1.5 million refugees from Ukraine have crossed into neighbouring countries in 10 days -- the fastest growing refugee crisis in Europe since World War II," the UN High Commissioner for Refugees, Filippo Grandi, tweeted.

According to the UN, four million people may seek to leave the country to escape the war.

Before the conflict, Ukraine had more than 37 million people in areas controlled by Kyiv -- which does not include Russian-annexed Crimea or separatist-controlled areas.

Ukraine evacuation
Over 1.5 million Ukrainians flee Russian invasion Photo: AFP / Sabrina BLANCHARD

Poland, which has championed the cause of Ukrainian refugees and where US Secretary of State Antony Blinken arrived on Saturday for talks with the country's top officials, is hosting by far the largest number of refugees arriving since the start of the Russian invasion.

In total, there were 885,303 refugees in Poland on Sunday, according to the UNHCR count -- 129,000 more than on Saturday and 57.7 percent of the total number recorded to have fled.

Polish border guards said they had registered 964,000 refugees by Sunday.

The number of arrivals reached a record 129,000 on Saturday. The vast majority were Ukrainians but the influx also included citizens of Afghanistan, Algeria, Belarus, India, Morocco, Nigeria, Pakistan, Poland, Russia, the United States and Uzbekistan.

Before the crisis, Poland was already home to about 1.5 million Ukrainians, most of whom came to work in the EU member state.

Ukrainian evacuees
Ukrainians have been crossing what remains of a destroyed bridge to reach Kyiv Photo: AFP / Aris Messinis

Hungary has taken in 169,053 people, or 11 percent of the total, and more than 12,000 more than the previous day, according to the UNHCR.

The country has five border crossings with Ukraine and several border towns, including Zahony, have turned public buildings into relief centres, where Hungarian civilians offer food or assistance.

Some 113,967 people have fled Ukraine for Slovakia, or 7.4 percent of the total, the UNHCR says.

Some 84,067 people, or 5.5 percent of the total, have crossed into Moldova, which US Secretary of State Antony Blinken was visiting on Sunday.

Prime Minister Natalia Gavrilita urged the US on Sunday to provide more humanitarian aid to help her country of 2.6 million, one of Europe's poorest, cope with the influx of people from Ukraine.

According to the UNHCR, some of the refugees are continuing on from Moldova to Romania or Hungary, often to reunite with family.

In Romania, the UNHCR has registered 71,640 refugees, or about 4.7 percent of the total.

Two camps have been set up, one in Sighetu Marmatiei and the other in Siret.

UNHCR also said that 157,056 people, around one in 10, had continued on to other European countries after crossing the Ukrainian border.

The number of people taking refuge in Russia remains unchanged at around 53,000, or 3.9 percent of the total.

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