The number of Ukrainian refugees could soon hit the one million mark, according to the U.N. refugee agency.

More than 874,000 people have fled Ukraine since Russia’s invasion last week, the agency reported Wednesday. That number is "rising exponentially" and could grow to a million in a matter of hours. 

The refugees are streaming into countries neighboring Ukraine, including Poland, Moldova, Hungary and Slovakia. 

People cross the Ukrainian border to Siret, Romania,

People cross the Ukrainian border to Siret, Romania, Wednesday, March 2, 2022, as they evacuate amid Russia´s invasion of Ukraine. (AP Photo/Fernando Llano) ((AP Photo/Fernando Llano)

The number of refugees has spiked quickly in the last few days. The United Nations’ refugee agency estimated on Sunday that 368,000 had fled the nation, before rising to 500,000 refugees on Monday. More than 200,000 people have fled the nation since Tuesday, UNHCR spokeswoman Shabia Mantoo said Wednesday.

"I have worked in refugee crises for almost 40 years and I have rarely seen such an incredibly fast rising exodus of people," UN High Commissioner for Refugees Filippo Grandi told the UN Security Council Monday.

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Russia and Ukraine have been battling for seven days as of Wednesday, leaving hundreds of transport facilities, hospitals, kindergartens and houses destroyed. 

Kyiv, Ukraine's capital, has been battered by shelling and attacks this week, including the bombing a TV tower and Babi Yar, the site of a massacre carried out by Nazi Germany, now a Holocaust memorial.

"This is beyond humanity," Ukrainian President Volodymyr Zelenskyy said Wednesday, according to a translation. "Such missile strike means that, for many Russians, our Kyiv is absolute foreign. They know nothing about our capital, about our history. They have orders to erase our history, our country and all of us."

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In Ukraine’s second-largest city, Kharkiv, dozens were killed and more than a hundred injured by shelling over the last day, regional governor Oleg Synegubov said Wednesday. A regional police and intelligence headquarters was also struck, according to the Ukrainian state emergency service.

The invading forces have are also pressing in on other towns and cities, including the strategic ports of Odesa and Mariupol.

Mariupol Mayor Vadym Boichenko reported mass casualties on Wednesday as the city suffers intense shelling from Russian forces. 

"The enemy occupying forces of the Russian Federation have done everything to block the exit of civilians from the city of half a million people," Mayor Vadym Boichenko said in a live broadcast on Ukrainian TV, Reuters reported. No exact casualty toll was provided. 

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"Today there are 128 people in our hospitals. Our doctors don't even go home anymore. They are fighting for the lives of Mariupol residents," Boichenko added. 

The Associated Press contributed to this report.