Ethiopia's Prime Minister Abiy Ahmed has said federal troops have begun the final phase of the operation in the northern Tigray state.
In a statement, he said "great care" would be taken to protect the 500,000 inhabitants of the region's capital, Mekelle, from harm.
But Mr Abiy warned residents to stay indoors.
He said that thousands of Tigrayan forces and militia had surrendered in the last 72 hours - but Tigray officials are yet to respond to the claim.
It has been difficult to verify claims from either side because of a communications blackout.
Mr Abiy had given Tigray forces a deadline to peacefully surrender which ended on Wednesday.
He rejected international interference in Ethiopia's internal issues and said the Tigray situation would be resolved in accordance to laws and international obligations.
The UN had asked the Ethiopian government to protect civilians ahead of the assault on Mekelle.