So far, the conflict between warring military factions that began in mid-April has caused nearly 600 000 people to escape into neighbouring countries including Egypt, Chad, South Sudan and Central African Republic.
"Unfortunately, looking at the trends, looking at the situation in Darfur, we're likely to go beyond 1 million," Raouf Mazou, UNHCR Assistant High Commissioner for Operations, said in response to a question about its estimate in April for the coming six months.
He was referring to ethnically motivated attacks and clashes in the Darfur region, which suffered a major conflict in the early 2000s killing some 300 000 people.
He did not give details on how far above 1 million he expected refugee numbers fleeing abroad to reach. The United Nations estimates more than 2.5 million people have been uprooted since April, most within Sudan.
The latest wave of violence in Darfur has been driven by militias from Arab nomadic tribes along with members of the Rapid Support Forces, a military faction engaged in a power struggle with Sudan's army in the capital, Khartoum, witnesses and activists said.
Witnesses told Reuters this month an increasing number of Sudanese civilians fleeing El Geneina, a city in Darfur hit by repeated attacks, have been killed or shot at as they tried to escape by foot to Chad.
He described access to refugees in Chad as "extraordinarily difficult" because the start of the rainy season was making it harder to reach refugees and move them away from the border into safer camps.
The UNHCR has already had to revise its forecast for people fleeing into Chad from Sudan to 245 000 from 100 000 people, he said.
"There's been less and less people wanting to stay at the border as the situation deteriorates in Darfur," he said.
MNA/PR