The UN refugee agency said in a statement on Friday that clashes in Ethiopia had prompted more than 14,500 people to flee into neighboring Sudan since early November.
Spokesman Babar Baloch said at a Geneva briefing earlier that more than 4,000 had crossed the border within 24 hours.
There are also concerns about a mass displacement of thousands of Eritrean refugees at a camp in Ethiopia.
Amnesty International said Thursday that scores of civilians were killed in a "massacre" in Ethiopia's Tigray region that witnesses blamed on forces backing the local ruling party in its fight against the federal government.
It was the first reported incident of large-scale civilian fatalities in a week-old conflict between the Tigray People's Liberation Front (TPLF) party and the government of Prime Minister Abiy Ahmed, winner of last year's Nobel Peace Prize.
The Amnesty report came the same day Abiy said government forces had made gains in western Tigray, and as Ethiopians continued to flee across the border into Sudan, stoking fears of a humanitarian crisis.
