The Ethiopian military plans to use tanks to encircle Mekelle, the capital of northern Tigray region, and is warning civilians it may also use artillery on the city, state media reported on Sunday.
In the beginning of November, fighting erupted between the Ethiopian federal government and the rebel TPLF party, which maintains de facto control of the Tigray region in the north. On Saturday it said Adigrat, about 116 km (72 miles) north of Mekelle, had also fallen.
Hundreds, possibly thousands of people have been killed, more than 30,000 refugees have fled into Sudan, and Tigrayan forces have fired rockets at Ethiopia's Amhara region and the neighbouring nation of Eritrea.
The Tigray region has been facing a rebellion since earlier this month.
The government and military could not immediately be reached for comment, but have previously repeatedly denied targeting civilians, saying they strike only TPLF targets.
AU President Cyril Ramaphosa of South Africa informed Ethiopia's President Sahle-Work Zewde on Friday that he had appointed former President of Mozambique Joaquim Chissano, former President of Liberia Ellen Johnson-Sirleaf, and former President of South Africa Kgalema Motlanthe as special envoys of the AU entrusted to facilitate negotiations between parties to end the conflict in Ethiopia.
But Ethiopia rebuffed the mediation efforts.
However it also contradicted Ramaphosa, saying, "News circulating that the envoys will be traveling to Ethiopia to mediate between the Federal Government and TPLF criminal element is fake".
He accuses them of revolting against central authority and attacking federal troops in the town of Dansha. The rebel leaders say Abiy's government has marginalised and persecuted Tigrayans since taking office two years ago.
Dejene said civilians in Mekelle, which has a population of half a million, should be aware of the danger.
Satellite images from US -based space company Maxar Technologies showed destroyed buildings lining the main road near Dansha airport, where the government says there was a November 4 surprise attack on federal troops. Abiy's parents are from the larger Oromo and Amhara ethnic groups.
The UN estimates that up to 200,000 could arrive in the coming months.
According to the Ethiopian government, on the way from Axum to Adwa, "the TPLF militia tried to defend itself in some areas, but was defeated by our defense forces who took full control of Adwa".
United Nations agencies are appealing for funding to aid more than 33,000 people fleeing violence in Ethiopia's Tigray region, fearing more than 200,000 could follow in six months, a spokesman for the world body said.