Ethiopia's Prime Minister Abiy Ahmed says government forces are now "fully in control" of Mekelle, the capital of the northern Tigray region.
He said the army had entered the city in the "last phase" of the conflict with the Tigray People's Liberation Front - but details are hard to confirm as there is a communications blackout.
The TPLF leader vowed to "fight... to the last" in a statement to Reuters.
Hundreds have reportedly been killed in the conflict and thousands displaced.
It began earlier this month after Mr Abiy announced an operation against the TPLF, the regional party, accusing it of attacking the Ethiopian army's northern command HQ in Mekelle.
Federal security forces are now searching for the TPLF leaders.
The BBC managed to briefly speak to one contact in Mekelle who said that federal soldiers were in the city and he had heard sporadic gunshots on Sunday morning. Some residents had earlier fled to the city's outskirts, he added.
Meanwhile, the US embassy in neighbouring Eritrea said six explosions were heard in the capital Asmara late on Saturday. Tigrayan forces have previously fired rockets at Eritrea, which they accuse of backing Ethiopian government forces in the weeks-long conflict. It is not clear if the latest incidents in Asmara are linked to the fighting in Tigray.
What does the government say?
In a statement on Twitter, Mr Abiy said the army was in full control of Mekelle and that this "marks the completion of the [military's] last phase".
"I am pleased to share that we have completed and ceased the military operations in the Tigray region," he said.
The army had released thousands of soldiers taken by the TPLF and was in control of the airport and regional offices, Mr Abiy said, adding that the operation had been carried out with "due care for citizens".
There have been fears for the safety of the 500,000 people living in the city.
Mr Abiy's statement said federal forces would "continue their task of apprehending TPLF criminals and bring them to the court of law".
Confirming details from Tigray is very hard as telephone and internet lines have been down during the conflict.
How has the TPLF responded?
In a text message to Reuters, TPLF leader Debretsion Gebremichael did not directly comment on the situation on the ground, but said of the government forces: "Their brutality can only add [to] our resolve to fight these invaders to the last."
He added: "This is about defending our right to self-determination."
Mr Debretsion's whereabouts are unknown.
A TPLF statement read out on regional Tigray TV said: "Fascistic bombings have caused civilian deaths and injuries. The Tigray government has vowed that it would take retaliatory actions against the barbaric bombings".
It also accused the Eritrean government of involvement in the attack on Mekelle.
Tigray TV and another station from the region are now off air.
Analysts say the TPLF could now be preparing to return to the mountains to launch a guerrilla war against the federal government.
What are the humanitarian concerns?
The UN had warned of possible war crimes if the Ethiopian army attacked Mekelle.
It has also expressed concerns about the lack of access for humanitarian workers.
The Ethiopian authorities said on Thursday that "a humanitarian access route" overseen by the government would be opened, adding they were "committed to work with UN agencies... to protect civilians and those who need it".
Also on Thursday, Ethiopian troops were deployed along Tigray's border with Sudan, preventing people fleeing the violence from leaving the country, according to refugees.
The BBC's Anne Soy, on the Sudanese side of the border, saw at least a dozen members of the Ethiopian military, leading to a marked decrease in the number of people crossing into Sudan.
In a meeting on Friday, Mr Abiy told African peace envoys that civilians would be protected.
However, there was no mention of potential peace talks and the envoys were not allowed to visit Tigray.
Who are the TPLF?
The TPLF fighters, drawn mostly from a paramilitary unit and a well-drilled local militia, are thought to number about 250,000. Some analysts fear the situation could turn into a guerrilla conflict - with the TPLF continuing to mount attacks on government forces even if they take Mekelle.
Mr Debretsion has said Tigray forces were "ready to die in defence of our right to administer our region".
Aid groups fear the conflict could trigger a humanitarian crisis and destabilise the Horn of Africa region.
Ethiopia's state-appointed Human Rights Commission has accused a Tigrayan youth group of being behind a massacre this month in which it says more than 600 non-Tigrayan civilians in the town of Mai-Kadra were killed. The TPLF denied involvement.
What is the fighting about?
The conflict is rooted in longstanding tension between Ethiopia's government and the TPLF, which was the dominant political force in the country until Mr Abiy came to power in 2018 and introduced far-reaching reforms.
When Mr Abiy postponed a national election because of coronavirus in June, relations further deteriorated.
The TPLF said the government's mandate to rule had expired, arguing that Mr Abiy had not been tested in a national election.
In September the party held its own election, which the government said was "illegal".