Some 60,000 - 90,000 people have fled into neighboring Chad since violence erupted last month, UNHCR, the U.N. refugee agency, said this week.
Tens of thousands have converged in a makeshift camp in a village named Borota where Pierre Kremer of the International Federation of the Red Cross and Red Crescent Societies (IFRC) was based last week.
"We know that we won't be able to relocate all of them before the rainy season," Kremer told a Geneva press briefing via video link from Nairobi. "It's a bit of a race now to relocate as many as we can... We run the risk of a major humanitarian disaster in this area."
Access to the area is expected to be difficult after the rainy season starts because large streams, known as wadis, are set to cut it off from supplies.
Some 80% of those arriving are women and children, many of whom have been separated from their parents as they fled from Darfur where violence between warring factions in the capital has spread in recent weeks.
Kremer said there had been reports of snake and scorpion bites among the refugees who are sleeping on the ground.
The UNHCR has said it is seeking to move refugees gathering in border areas to pre-existing refugee camps in Chad and establish five new ones.
A UNHCR spokesperson in Chad, Eujin Byun, told Reuters that many of the refugees reported losing family members and having their homes burned down. Teenagers were often travelling alone with infants, she said.
"I'm overwhelmed to see them," she said. "It's a lot of children and it's really heartbreaking as they don't know where their parents are."