Federal government has said its troops have seized Adigrat town, a distance of 120 kilometres from the Tigrayan capital of Mekelle. Government forces had earlier taken control of the towns of Axum and Adwa,
Ethiopian forces have seized another town in their advance on the capital of northern Tigray region and rebuffed an African Union (AU) push to mediate in the war with rebel forces in the region.
Rebels in north Ethiopia said that nine people had died among heavy civilian casualties during the offensive by Prime Minister Abiy Ahmed's federal troops on the town of Adigrat. The statement could not be independently verified.
The government and military could not immediately be reached for comment, but have previously denied targeting civilians.
Hundreds, possibly thousands, have died and more than 30,000 refugees have fled to Sudan. The conflict has spread beyond Tigray, whose forces have fired rockets at the neighbouring Amhara region and the nation of Eritrea, spurring concern of a wider war.
Abiy's government has said it will soon reach regional capital Mekelle after taking various surrounding towns. On Saturday it said Adigrat had also fallen.
There was no immediate response from the Tigray People's Liberation Front (TPLF) rebels who have promised "hell" for the advancing federal troops. The TPLF had said on Friday its forces were making progress on the southern and northern fronts.
Assertions on all sides are hard to verify because phone lines and internet have been down since the beginning of the conflict on Nov. 4 and media are largely barred.
Fall of Axum and Adwa
Government forces have taken control of the towns of Axum and Adwa, a government statement said earlier.
Tigrayan forces were not available for comment but in a televised address, spokesman Getachew Reda said their fighters have inflicted "increasing casualties" in Raya, to the south of Mekelle.
Tigray an fighters also "eliminated enemy forces" from Mehoni in the south and Zalambessa to the northeast, Tigrayan TV said.
A government spokesman did not return calls seeking comment.
Reda's address also claimed responsibility for a rocket attack in the early hours of Friday on the airport in Bahir Dar, which Amhara authorities had announced earlier in the day.
He said it was in retaliation for bombing raids launched from there.
"We will continue to target whichever airport has been used to stage an attack on Tigray," he said.
The Amhara government's communications office said the rockets caused no damage.
Bahir Dar, Amhara's lakeside capital, is located hundreds of miles from the fighting in Tigray. Tigrayan refugees have told Reuters that Amhara militiamen are fighting on the government side. The two regions also have a border dispute.
At the Um Rakuba settlement in Sudan, where aid workers are setting up a camp in the scrubland for 10,000 mai nly Tigrayan refugees, those who arrived queued up for corn flour porridge and put up makeshift shelters.
Yohannes Gor, 28, arrived by foot after fleeing the Ethiopian town of Humera, close to the border, 10 days ago with only the clothes he was wearing.
"I live under this tree and sleep on the dirt," he said. "I lost all trace of my family and I don't know what happened to them."
Aid agencies fear a humanitarian emergency in Tigray, where hundreds of thousands of people depended on relief aid even before the conflict. Refugees have crowded into boats to cross a river to Sudan, overwhelming aid groups on the other side.
Axel Bisschop of the UN refugee agency UNHCR told a briefing in Geneva that 31,000 refugees had already reached Sudan, surpassing a contingency plan for 20,000. "The new planning figure is around 200,000."
UNICEF's Sudan-based representative Abdullah Fadil worried about the impact on Sudan, already hosting 1 million refugees from other African wars.
"Our serious concern is if we do not act quickly with the resources needed...this could unravel not only Ethiopia but also Sudan," he told the same briefing.
Ethiopia, a federation of 10 ethnic regions, was dominated for decades by Tigrayans in a TPLF-led ruling coalition, until Abiy, who is of Amhara and Oromo descent, took power two years ago.
He says he aims to share authority more fairly. The TPLF accuses him of pursuing a vendetta against former officials.
The conflict erupted two weeks ago after what the government called a TPLF attack on army forces stationed in the region.
Tigray forces blame government for university bombing
On Thursday, Tigray forces accused the government of bombing a university in the Tigray capital Mekelle. There was no immediate response from the government, although officials have said they are attacking only military targets.
A week ago, Tigray forces fired rockets at two airports in Amhara. They have also fired rockets into the neighbouring nation of Eritrea, which has a long-running enmity with the TPLF leadership. Eritrea made peace with Ethiopia in 2018, earning Abiy the Nobel Peace Prize.
Reports of ethnically motivated killings have emerged. Rights group Amnesty International documented a mass killing of civilians, many of whom appeared to be Amhara, by what it says were Tigrayan forces on Nov. 9-10. The Tigray authorities have denied this.
Refugees fleeing into Sudan have said they were targeted for being Tigrayan.
Since taking power, Abiy has freed political prisoners and loosened what was once one of Africa's most repressive political and economic systems. But the new freedoms have been accompanied by violence as regional bosses vie for power, money and land.