"Without a quick resolution of this crisis we will continue to see more people forced to flee in search of safety and basic assistance," the UN's Raouf Mazou told a member state briefing in Geneva.
"In consultation with all concerned governments and partners we've arrived at a planning figure of 815,000 people that may flee into the seven neighboring countries."
The estimate includes around 580,000 Sudanese, he said, with the others existing refugees from South Sudan and elsewhere.
So far, he said some 73,000 people have already fled to Sudan's neighbours - South Sudan, Chad, Egypt, Eritrea, Ethiopia, Central African Republic and Libya.
U.N. aid chief Martin Griffiths will visit Sudan on Tuesday, said Ramesh Rajasingham of the U.N. Office for the Coordination of Humanitarian Affairs.
Griffiths was in Nairobi, Kenya, on Monday to discuss the situation in Sudan, which he described as "catastrophic."
"We need to find ways to get aid into the country and distribute it to those in need," Griffiths wrote on Twitter.
In separate comments, the United Nations humanitarian coordinator in Sudan said the humanitarian crisis was turning into a "full blown catastrophe" and that the risk of spillover into neighboring countries was worrying.
"It has been more than two weeks of devastating fighting in Sudan, a conflict that is turning Sudan humanitarian crisis into a full blown catastrophe," Abdou Dieng told member states via video link.