Ethiopia's prime minister has said a military operation against rebel forces in the northern Tigray region is entering its "final phase".
Abiy Ahmed said a three-day deadline given for Tigray's forces to surrender had now expired.
Hundreds of people have reportedly died in nearly two weeks of clashes between the rebels and the federal army. At least 27,000 people have fled to Sudan.
The UN has said a "full-scale humanitarian crisis" is unfolding.
Getting information from Tigray is hard as there is a virtual communications blackout.
Fighting broke out on 4 November after Ethiopia's central government accused the Tigray People's Liberation Front (TPLF), a political party which controls Tigray, of holding an illegal election and attacking a military base to steal weapons. The TPLF has denied the attack.
In response, Mr Abiy ordered a military offensive against forces loyal to the regional government of Tigray, accusing them of treason. He said that "the last red line had been crossed".
The TPLF sees the central government as illegitimate, arguing Mr Abiy does not have a mandate to lead the country after postponing national elections because of coronavirus.
Is the fighting coming to an end?
Ethiopia said its forces are marching on Tigray's capital Mekelle after making major military gains, and accused Tigrayans of destroying bridges en route to the city. The Tigrayans say they are defending the town of Alamata, which lies on the road north to Mekelle.
In a Facebook post, Mr Abiy said the operation by the federal forces was nearing a conclusion.
"The final critical act of law enforcement will be done in the coming days," the prime minister said.
He thanked TPLF fighters who, he said, had taken advantage of the deadline to switch sides but he did not give a number.
And Mr Abiy added that his government was "ready to receive and reintegrate our fellow Ethiopians fleeing to neighbouring countries".
Meanwhile, TPLF adviser Fesseha Tessema, a former Ethiopian diplomat, told the BBC that civilian sites in Mekelle were being bombed by federal forces.
"[The people of Tigray] haven't done anything wrong, they are in their own homes, churches," Mr Fesseha said.
The federal government has denied targeting civilians and said that air attacks are aimed at the Tigrayan military.
How bad is the humanitarian crisis?
The UN's refugee agency, the UNHCR, has said that "a full-scale humanitarian crisis is unfolding" and thousands have been fleeing the fighting.
The agency was "on stand-by to provide assistance in Tigray when access and security allow" spokesman Babar Baloch said.
"There may be massive displacement inside Tigray and that is of course a concern and we try to prepare the best way possible," Jens Laerke, spokesman of the UN Office for the Coordination of Humanitarian Affairs (OCHA), said.
The UN fears the numbers fleeing Ethiopia may be just a fraction of those forced from their homes by the fighting, but for the moment aid agencies have no access to the Tigray region.
Regional powers Kenya and Uganda have called for negotiations to find a peaceful resolution to the conflict.
The Ethiopian government has, however, ruled out talks with the TPLF.
How bad is the violence?
Hundreds have reportedly been killed.
Human rights group Amnesty International said it had confirmed that "scores, and likely hundreds, of people were stabbed or hacked to death" in the town of Mai-Kadra (May Cadera) on Monday last week.
Mr Abiy has accused forces loyal to Tigray's leaders of carrying out the mass killings. The TPLF has denied involvement, saying it will welcome an independent international investigation.
Ethiopia's human rights commission said it would send a team to investigate.
Why are the government and TPLF fighting?
The TPLF dominated Ethiopia's military and political life for decades before Mr Abiy took office in 2018 and pushed through major reforms.
Last year, Mr Abiy dissolved the ruling coalition, made up of several ethnically based regional parties, and merged them into a single, national party, which the TPLF refused to join.
The feud escalated in September, when Tigray held a regional election, defying a nationwide ban on all polls imposed because of the coronavirus pandemic. Mr Abiy responded by calling the vote illegal.
Tigray's administration sees Mr Abiy's reforms as an attempt to hand his central government more power and weaken regional states.
It also resents what it calls the prime minister's "unprincipled" friendship with Eritrean President Isaias Afwerki.
Mr Abiy won the Nobel Peace Prize in 2019 for his efforts to bring peace with Eritrea.
The prime minister believes TPLF officials are undermining his authority.