Ethiopian Prime Minister Abiy Ahmed gave Tigrayan regional forces 72 hours to surrender before the military begins an offensive on the regional capital of Mekelle.
"We urge you to surrender peacefully within 72 hours, recognising that you are at the point of no return," Mr Abiy said on Twitter on Sunday evening.
Tigrayan forces could not immediately be reached for comment.
An Ethiopian military spokesman said earlier that advancing troops planned to surround Mekelle with tanks and may shell the city to force surrender.
The Tigray People's Liberation Front, which is refusing to surrender its rule of the northern region, said its forces were digging trenches and standing firm.
Claims by both sides are hard to verify because phone and internet communication has been down.
Mr Abiy's federal troops have taken a string of towns during aerial bombardments and ground fighting, and are now aiming for Mekelle, a highland city of about 500,000 people, where the rebels are based.
The conflict erupted on November 4 and has killed hundreds, possibly thousands, and has sent more than 30,000 refugees feeling into neighbouring Sudan.
Rockets have been fired by rebels into neighbouring Amhara region and across the border into Eritrea.
Mr Abiy said "all the necessary precautionary measures have been taken to ensure that civilians are not harmed".
"All that the clique is left with is the fort that they have set up in Mekelle and empty pride," he said.
Mr Abiy said the people of Tigray had had enough of rebel violence against them, and appealed to the people of Mekelle to stand with the federal troops in "bringing this treasonous group" to justice.
He accuses Tigrayan leaders of revolting against the central authority and starting the conflict by attacking federal troops in the town of Dansha on November 4.
The rebels say 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 next phases are the decisive part of the operation, which is to encircle Mekelle using tanks," military spokesman Col Dejene Tsegaye told the state-run Ethiopia Broadcasting Corporation earlier on Sunday.
Col Dejene said the TPLF leadership was "shielding itself within the public".
"We want to send a message to the public in Mekelle to save yourselves from any artillery attacks and free yourselves from the junta," he said.
Rebel leader Debretsion Gebremichael said 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," Mr Gebremichael 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 drew plaudits for opening up Ethiopia's closed economy and repressive political system after taking office in 2018.
He won a Nobel Peace Prize last year for ending a two-decade standoff with Eritrea.
The awarding committee in Oslo last week made a rare foray into the activities of laureates by urging peace in Tigray.
Redwan Hussein, spokesman for the government's taskforce on Tigray, said there was still time for rebel leaders to surrender.
"The government will take maximum restraint not to cause major risks for civilians," Mr Hussein said.
He said that while many Tigrayan special forces and militiamen had surrendered or scattered around Adigrat, resistance was stronger on the southern front where rebels have dug up and booby-trapped roads, and destroyed bridges.
The taskforce added that the army had also taken the small town of Idaga Hamus on the road from Adigrat to Mekelle.
