Rebels from Ethiopia’s northern Tigray region have taken control of the town of Lalibela, a Unesco world heritage site in neighbouring Amhara region.
Lalibela, home to 13th Century churches hewn from rock, is a holy site for millions of Orthodox Christians.
Residents have been fleeing the rebel advance, local officials told the BBC.
Thousands have been killed since war broke out last November. Fighting is now spreading into Amhara and Afar, another region bordering Tigray.
Millions of people have also been displaced.
Both the Tigray rebel forces and the Ethiopian army and its allies have been accused of committing human rights abuses and war crimes.
The deputy mayor of Lalibela, Mandefro Tadesse, told the BBC that the town was under the control of the Tigray rebels.
He said there had not been any shooting, but residents were fleeing from the town and he was concerned about the safety of the historic churches.
There are 11 medieval monolithic cave churches carved out of rock that date from the 12th and 13th Centuries. They were built as a substitute for pilgrimages to the Holy Land, which was unreachable at the time.
“This is the world’s heritage, and we must cooperate to guarantee that this treasure is preserved,” Mr Mandefro said.
The spreading fighting follows significant territorial gains made by the rebel Tigray People’s Liberation Front (TPLF) in June, including capturing the Tigray regional capital Mekelle after Ethiopian troops withdrew and the government declared a unilateral ceasefire.
The TPLF was the regional government of Tigray until it was ousted by federal forces last November.
It has been designated a terrorist organisation by the Ethiopian government.
However, the rebels say they are the legitimate regional government of Tigray.
Earlier this week a rebel general told the BBC that the group aimed to force the federal government to lift a blockade in the region and agree to a political solution to the crisis.
The government denies there is a blockade and has ruled out talks.
However the TPLF’s push into Amhara and Afar has drawn international criticism, and both the UN and the US this week called for all parties to stop fighting.
The Ethiopian government says more than 300,000 people have been displaced in Amhara and Afar.
Separately the UN said 175 lorries carrying humanitarian aid had arrived in Tigray.
But the head of the UN’s World Food Programme (WFP) warned that more than 100 lorries were needed every day to reach the millions who were in need.
Aid workers have struggled to get access to much of Tigray due to insecurity and bureaucratic hurdles.