Government-allied fighters entered Mekelle, the capital of Ethiopia's northern Tigray region, a witness said, after the rebel Tigray People's Liberation Front (TPLF) announced its withdrawal.

The TPLF, which last month seized Mekelle's airport, said in a statement on Saturday that it had pulled out of the city following renewed fighting.

They had done so in the previous two-year civil war, which ended with a 2022 peace agreement, apparently to prevent the city being destroyed.

The TPLF statement added the regional government would be "temporarily moved out of Mekelle and operate from somewhere else".

Ethiopian federal forces had taken the airport in the city, people in the city told The Associated Press on Saturday, reversing a takeover by the Tigrayan fighters that prompted the suspension of commercial flights in September.

A source close to the pro-government militia, the Tigray Peace Forces, said its fighters entered the centre of the city on Saturday afternoon, followed by the Ethiopian military.

The African Union has urged restraint amid heightened tensions, warning that the fighting could derail the 2022 agreement.

A humanitarian source and Mekelle resident, who asked not to be named, confirmed the city is now under control of government forces.

Prime Minister Abiy Ahmed has failed to quieten tensions with Tigray's rebellious leaders in recent months, with TPLF chairman Debretsion Gebremichael openly challenging him.

He said on Thursday that the fighting was a "continuation of the previous war" and that his troops would keep attacking and defending Tigray.

The Tigray Peace Force is fighting alongside federal troops against the TPLF.

In Mekelle, civilians looted government offices and stole equipment from police headquarters as TPLF-allied fighters withdrew, a local business owner said on Sunday.

The looting targeted the TPLF administration office, the regional police headquarters, and some shops, Filmon Equar Hailu said.

Departures started in small groups around three days ago and continued through Saturday afternoon, he added.

The TPLF is one of seven opposition groups that declared an alliance late last month to remove Mr Abiy, who came to power in 2018, and was re-elected earlier this year. More from Sky News: Crews find 'debris field' in search for missing plane What we know about co-pilot accused of trying to hijack plane The conflict is also testing regional alliances, with Ethiopia saying the TPLF is likely being supported by Eritrea and Egypt.

Ethiopia on Thursday closed its embassy in Eritrea and ordered 10 Eritrean diplomats to leave Addis Ababa, the federal capital, citing their alleged "involvement in activities that pose a direct threat to Ethiopia's national security". Eritrea responded by saying it was cutting diplomatic ties with its neighbour.

Egypt denies supporting the TPLF, and Eritrea says Mr Abiy is trying to externalise an internal conflict.

The fighting has sparked fears that it could fan out into a wider regional conflict, potentially drawing in neighbouring countries in the Horn of Africa and the Gulf.

In Washington, state department spokesman Tommy Pigott said the US strongly urged Ethiopia and Eritrea to "exercise maximum restraint and return to dialogue and cooperation as agreed in their 2018 peace framework".