The refugees told a U.N. team in the northeastern town of Sam-Ouandja, some 80 km (50 miles) from the Sudanese border, that a ground and air attack had forced all 15,000 inhabitants of the southern Darfur town of Dafak to flee their homes.
Most of them headed south within Sudan, but some fled westward into Central African Republic, an arduous journey of more than 200 kilometres (125 miles) following a track accessible only on foot or by horse.
Their flight was the latest evidence that the conflict in Darfur, where a war pitting rebels against Sudan's army and allied militias has raged since 2003, is pushing refugees into neighbouring states like Chad and Central African Republic.
"So far we have registered 1,411 refugees and more of them are arriving every day," said Bruno Geddo, country representative for the U.N. refugee agency UNHCR, who led a U.N. mission on Monday to Sam-Ouandja in the isolated north-east.
"We are working on an estimate of 3,000 (refugees) at the moment," he told Reuters.
Although initial news reports suggested the group were armed and could include Chadian rebels, Geddo said the U.N. team had found no evidence of either weapons or Chadian nationals.
The town of Sam-Ouandja was attacked in March and November by insurgents trying to topple Central African President Francois Bozize, who seized power in a 2003 coup before legitimising his rule at the ballot box two years later.
Geddo said the town's inhabitants were unable to cope with the influx of Sudanese refugees, who were currently relying on mangoes picked from the bush for food.
The United Nations children's agency UNICEF estimated last month that a quarter of the 4 million people in Central African Republic -- the world's sixth poorest country -- are suffering the effects of internal violence or the spill over from conflicts in neighbouring Sudan and Chad.
- Reuters - Thomson Reuters Foundation
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