The Tigray forces on Tuesday announced that they had "completely destroyed" the 21st mechanised division of the Ethiopian Army.
The Ethiopian government has not commented on the claim yet.
Earlier in the day, Alsir Khaled, the head of Sudan's refugee agency in the eastern border town of Kassala, said that more than 45,000 people had fled Ethiopia since the start of the armed conflict in the Tigray region.
In November, an armed conflict started between Ethiopia’s government and the Tigray People's Liberation Front (TPLF) after the government accused Tigray forces of conducting an attack on a military base in the region.
On Sunday, Ethiopian Prime Minister Abiy Ahmed said that TPLF rebels had three days to "surrender peacefully" and called on civilians in the capital of the Tigray region, Mekelle (Mekele), to stand in solidarity with the government forces.
The Ethiopian forces have already seized the cities of Igada Hamus, Adigrat and Axum, as well as the town of Adwa.