Tigray’s leader confirmed the losses but said it was a temporary setback and vowed to defeat the government.
Ethiopia’s prime minister has said that his army is advancing on the Tigrayan capital Mekelle.
Hundreds of people have reportedly died in two weeks of clashes.
The conflict is rooted in long-standing tension between powerful regional party the Tigray People’s Liberation Front (TPLF) and Ethiopia’s central government.
When Ethiopian Prime Minister Abiy Ahmed postponed a national election due to coronavirus in June, tension escalated between the two groups. The TPLF sees the central government as illegitimate, arguing Mr Abiy no longer has a mandate to lead the country.
The government accused the TPLF of attacking a military base to steal weapons, which the TPLF denied. In response, Mr Abiy ordered a military offensive, accusing the TPLF of treason.
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Government forces seized the towns of Shire and Axum after a three-day deadline given by Prime Minister Abiy to Tigray’s forces to surrender expired on Tuesday.
TPLF leader Debretsion Gebremichael, who was born in Shire, confirmed to a local TV station that his soldiers had lost control of the towns in the south and west of Tigray. But he said their victory was temporary and he vowed to defeat Mr Abiy’s forces.
As fighting raged on Wednesday, Mr Gebremichael said his forces were inflicting “heavy defeats on all fronts against the forces that came to attack us”. He called on all Tigrayans including children to mobilise and join the “struggle”.
Ethiopian officials accused the TPLF of destroying four bridges close to the Tigray capital Mekelle, but the group denied the claims.
The prime minister suggested on Tuesday that the fighting was coming to an end, saying “the final critical act of law enforcement will be done in the coming days”.
TPLF adviser Fesseha Tessema, a former Ethiopian diplomat, told the BBC that civilian sites in Mekelle were being bombed by federal forces.
“[The people of Tigray] haven’t done anything wrong, they are in their own homes, churches,” Mr Fesseha said.
The federal government has denied targeting civilians and said that air attacks are aimed at the Tigrayan military.