The government accused Tigray's forces of destroying bridges near the city of Mekelle to halt the advance.
Hundreds of people have reportedly died in nearly two weeks of clashes.
Verifying information from Tigray is hard due to a blackout on most communications.
Prime Minister Abiy Ahmed 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."
The conflict is rooted in long-standing tension between powerful Tigrayan party the Tigray People's Liberation Front (TPLF) and Ethiopia's central government.
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