There was no immediate comment from Tigray's leaders on the events in Alamata, a town near the border with Amhara regional state and around 120 km from Tigray's capital Mekelle.
Ethiopia has said its federal forces have liberated a town in the northern Tigray region, where it accused local leaders of taking 10,000 prisoners with them from the town as they fled.
"As the TPLF (Tigray's ruling party) militia were defeated in Alamata, they fled taking along around 10,000 prisoners," the government's taskforce said on Twitter.
There was no immediate comment from Tigray's leaders on the events in Alamata, a town near the border with Amhara regional state, about 120 km (75 miles) from Tigray's capital Mekelle.
Earlier on Saturday, Tigray forces had fired rockets into neighbouring Eritrea, escalating a 13-day conflict which has killed hundreds on both sides, and threatens to destabilise other parts of Ethiopia and the Horn of Africa.
With access restricted and most communications down in Tigray, Reuters could not independently verify assertions made by all sides.
The US State Department's top diplomat for Africa, Tibor Nagy, denounced the attacks by Tigrayan forces on Eritrea, calling them "efforts to internationalise the conflict" in Tigray.
The United States strongly condemns the TPLF’s unjustifiable attacks against Eritrea on November 14 and its efforts to internationalize the conflict in Tigray. We continue to urge immediate action to protect civilians, deescalate tensions, and restore peace.— Tibor Nagy (@AsstSecStateAF) November 15, 2020
Debretsion Gebremichael, Tigray's regional president, has accused Eritrea of sending tanks and thousands of troops into his region in support of the Ethiopian government's offensive.
Eritrea's Foreign Minister Osman Saleh Mohammed told Reuters last week that his country was not involved in the conflict.
READ MORE: Is Ethiopia headed for a protracted war?
Abiy launched the campaign in Tigray on November4 after accusing local forces of attacking federal troops based in the northern state, which borders Eritrea and Sudan and is home to some 5 million people.
Fighting spread into Ethiopia's Amhara state, whose local forces are fighting with federal troops in Tigray. Late on Friday, rockets were fired at two airports in Amhara in what the TPLF said was retaliation for government air strikes.
The government says the strikes aim to destroy equipment controlled by insurgent Tigray forces.
At least 20,000 Ethiopians have fled into Sudan, the United Nations said on Sunday.