Ethiopia says that its forces have made major military gains in northern Tigray and are marching on the regional capital, Mekelle.
The Tigrayan insurgents say they are putting up resistance at another town, Alamata.
Refugees from the region are continuing to pour into Sudan, giving harrowing accounts of bodies dismembered by explosions or people being hacked to death.
Many are displaced within Tigray, less than two weeks after war broke out.
The UN Emergency Relief Coordinator, Mark Lowcock, said those people were suffering shortages of food and fuel, but that a communications blackout in the region meant the humanitarian agency had limited access.
The UN refugee agency has warned of a “full-scale humanitarian crisis”.