A spokeswoman describes the refugees as "destitute and terrified." She says they are telling stories of villages being encircled by militia, looted and burned.
The agency says most of the refugees so far are men, and those men are telling U.N. officials that "thousands of women and children are on their way" to Chad.
U.N. officials say the worsening situation in Darfur has been exacerbated by a recent rebel attack on the capital of Chad.
