Ethiopian federal forces were encircling the Tigray region's capital from around 50 km (31 miles) on Monday, the government said, after giving the Tigray People's Liberation Front (TPLF) a 72-hour surrender ultimatum.
"The beginning of the end is within reach," said government spokesman Redwan Hussein of the nearly three-week offensive that has destabilised both Ethiopia and the wider Horn of Africa.
Prime Minister Abiy Ahmed has told the TPLF, which had been ruling the mountainous northern zone of 5 million people, to lay down arms by Wednesday or face a final assault on Mekelle.
TPLF leader Debretsion Gebremichael told Reuters that threat was a cover for government forces to regroup after what he described as defeats on three fronts.
Reuters could not verify the latest statements.
Claims by all sides are hard to verify because phone and internet communication has been down.
Hundreds, possibly thousands, have been killed in fighting and air strikes that erupted on Nov. 4, sending about 40,000 refugees into neighbouring Sudan. The conflict has spread beyond Tigray, with the TPLF firing rockets into both neighbouring Amhara region and across the border to Eritrea.
Redwan told Reuters by text that federal forces were ringing Mekelle at a distance of about 50 km (30 miles).
Tigrayan forces fired rockets on Monday at Bahir Dar, the capital of neighbouring Amhara region whose authorities are supporting the federal offensive, he also said.
"So far, I didn't hear of any casualties," said a hotel receptionist in the lakeside city where residents reported a pre-dawn rocket attack. "I guess now we are accustomed to it and there wasn't much panic."
TPLF troops had also destroyed the airport at the ancient town of Axum, a popular tourist draw and UNESCO World Heritage site which lies northwest of Mekelle, Redwan said.
Axum's history and ruins, including fourth century obelisks when the Axumite Empire was at its height, gives Ethiopia its claim to be one of the world's oldest centres of Christianity.
Legend says it was once home to the Queen of Sheba and Ethiopians believe a church there houses the Ark of the Covenant.
The TPLF says Abiy has "invaded" their region to dominate them and is inflicting "merciless" damage on Tigrayans.
"We are people of principle and are ready to die in defence of our right to administer our region," TPLF leader Debretsion added in a text message to Reuters. Debretsion was a signals and intelligence officer for the TPLF during their war against the Communist Derg dictatorship in the 1980s and later earned a degree in electronic engineering from Addis Ababa University.
He rose to the rank of deputy prime minister in the Ethiopian government when it was dominated by the TPLF.
The TPLF accuses accuse Abiy, a former military comrade and partner in government, of marginalising their ethnic group since becoming prime minister two years ago. He has removed Tigrayan officials from influential roles in government and the military and detained some on rights abuse and corruption charges.
Abiy, whose parents are from the larger Oromo and Amhara groups, denies any ethnic undertones, saying he is legitimately pursuing criminals and preserving national unity.
The African Union (AU) has appointed three envoys to try and start mediation talks over Tigray. Redwan said Abiy would meet them and all options were on the table except negotiating with the TPLF "gang".
The United Nations' humanitarian coordinator for Ethiopia, Catherine Sozi, urged safety guarantees for aid workers, Mekelle's more than half a million inhabitants, and their health, school and water systems.
