More than 4 million Ukrainians have now fled the country to escape Russia's "senseless war," the United Nations said Wednesday.

The U.N. High Commissioner for Refugees (UNHCR) posted Wednesday on a website that tracks refugee flows around the world that 4.01 million people have now fled Ukraine. Of those, 2.3 million have entered Poland.

Aid workers say the flow has eased in recent days as many people await developments in the war. An estimated 6.5 million people have also been displaced from their homes within Ukraine, according to the Associated Press (AP).

"Refugees from Ukraine are now four million, five weeks after the start of the Russian attack," UNHCR chief Filippo Grandi said on Twitter. "I have just arrived in Ukraine. In Lviv I will discuss with the authorities, the UN and other partners ways to increase our support to people affected and displaced by this senseless war."

The number of refugees has surpassed UNHCR's initial estimate that the war could create up to 4 million.

The agency says the speed and scale of the displacement is unprecedented in Europe since World War II.

Women and children account for 90% of those who have fled. Ukrainian men aged 18 to 60 are eligible for military call-up and cannot leave.

The U.N.'s International Organization for Migration (IOM) said that in addition to Ukrainian refugees, close to 200,000 non-Ukrainians living, studying and working in the country have also left.

And as of March 16, some 6.48 million people were estimated to be internally displaced within Ukraine, according to an IOM representative survey.

"They need urgent life-saving aid," the organization said Wednesday.

"In response to the war in Ukraine, IOM has scaled up its effort to prevent the trafficking of persons both in the country and among those moving throughout the region," it added.

Before Russia's Feb. 24 invasion, Ukraine had a population of 37 million in the regions under government control, excluding Russia-annexed Crimea and the pro-Russian separatist regions in the east.