According to the U.N. Refugee Agency, the current total of the refugees out of Ukraine is now up to 368,000 with the numbers still rapidly rising.
Border authorities in Poland said that around 100,000 people had arrived in recent days, the U.N. Office for the Coordination of Humanitarian Affairs said. Others have traveled to Moldova and Romania, it added.
"While the scale and scope of displacement will only likely become apparent in the coming days and weeks, Ukrainian authorities estimate that as many as 5 million people could flee the country," the agency said in a report Saturday evening.
Inside Ukraine, the report said that "significant infrastructural damage has left hundreds of thousands of people without electricity or water, while bridges and roads damaged by shelling have left communities cut off from markets for food and other basic supplies."
Get Philly local news, weather forecasts, sports and entertainment stories to your inbox. Sign up for NBC Philadelphia newsletters.
In Ukraine's eastern Donbas region where Russian-backed separatist forces have been battling the Ukrainian military since 2014, the report said that the current situation was "exacerbating an already dire humanitarian situation" and "generating new multisectoral needs across the country."
This is a live update. Click here for complete coverage of the crisis in Ukraine.