Ethiopian civilians have been urged to "save themselves" as advancing federal troops plan to surround the capital of the restive Tigray region with tanks in a bid to force opposition forces to surrender.
But the Tigray People's Liberation Front (TPLF), which is refusing to surrender its rule of the northern region, said its forces were digging trenches and standing firm.
Prime Minister Abiy Ahmed's federal troops have taken a string of towns during aerial bombardments and ground fighting, and are now aiming for the capital Mekelle, a highland city of about 500,000 people where the rebels are based.
Mr Abiy has given TPLF forces 72 hours to surrender before the military begins an offensive.
"We urge you to surrender peacefully within 72 hours, recognising that you are at the point of no return," Mr Abiy said in a Twitter message on Sunday evening.
Tigrayan forces could not immediately be reached for comment.
The war has killed hundreds, possibly thousands of people, sent more than 30,000 refugees into neighbouring Sudan, and seen rockets fired by rebels into the neighbouring Amhara region and across the border into the nation of Eritrea.
Foreign nations have urged talks over what the United Nations has called a "full-scale humanitarian crisis", but Mr Abiy has pressed on with the offensive since November 4.
Claims by all sides are hard to verify because the Ethiopian Government has shut off communications in Tigray.
"The next phases are the decisive part of the operation, which is to encircle Mekelle using tanks," military spokesperson Colonel Dejene Tsegaye told state-run Ethiopia Broadcasting Corporation.
TPLF leader Debretsion Gebremichael told Reuters by text message that his forces were resisting a push from the south while also fighting near the northern town of Adigrat after it fell to federal troops.
"Encircling Mekelle is their plan but yet they couldn't," he said.
"On south front, they couldn't move an inch for more than one week.
"They [are] sending waves after waves but to no avail."
Mr Abiy has accused the Tigrayan leaders of revolting against the Federal Government and starting the conflict by attacking troops in the town of Dansha.
But the rebels have said his Government has marginalised Tigrayans since taking office two years ago, removing them from senior roles in government and the military and detaining many on rights abuse and corruption charges.
The Prime Minister drew plaudits for opening up Ethiopia's closed economy and repressive political system after taking office, which included winning the 2019 Nobel Peace Prize for ending a two-decade standoff with neighbouring Eritrea.
However, rights groups have said his Government has carried out mass arrests after outbreaks of violence and detained journalists this year.
Redwan Hussein, a spokesperson for the Government's taskforce on Tigray, contrasted with Colonel Tsegaye's threats of "no mercy", and said there was still time for TPLF leaders to surrender.
While many Tigrayan special forces and militiamen had surrendered or scattered around Adigrat, resistance was stronger on the southern front, Mr Redwan said, where rebels have dug up roads, destroyed bridges and booby-trapped roads.
The taskforce added that the army had also taken the small town of Idaga Hamus on the road from Adigrat to Mekelle.