One million refugees have fled Ukraine in the week since Russia's invasion, the United Nations said Thursday, warning that unless the conflict ended immediately, millions more were likely to flee.  

"In just seven days we have witnessed the exodus of one million refugees from Ukraine to neighbouring countries," UN refugee chief Filippo Grandi tweeted.

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

According to frequently updated UNHCR data, 1,002,860 have now fled Ukraine since Russian President Vladimir Putin launched the full-scale invasion on February 24.

Grandi said the numbers were rising with incredible speed.

"I have worked in refugee emergencies for almost 40 years, and rarely have I seen an exodus as rapid as this one," he said.

"Hour by hour, minute by minute, more people are fleeing the terrifying reality of violence," he said.

More than half of those who have fled Ukraine have crossed into neighbouring Poland. Hungary, Moldova, Hungary and Slovakia have also welcomed many refugees.

The UNHCR said more than 505,500 people have left Ukraine for Poland in the past week. Poland's border guards put the figure at over 575,000 by early Thursday, with 95,000 having crossed on Wednesday alone.

Countless people have also been displaced inside the Ukraine.

Grandi said UNHCR staff and other humanitarians were "working where and when they can in frightening conditions" inside Ukraine.

"Our staff stay, even at great risk, because we know the needs in the country are huge."

The UN refugee chief also hailed the "remarkable" response of governments and local communities in surrounding countries that have received the more than one million refugees.

"International solidarity has been heart-warming," he said.

"But nothing – nothing – can replace the need for the guns to be silenced; for dialogue and diplomacy to succeed. Peace is the only way to halt this tragedy."