The development came as a senior Amhara official says the rebels, known as the Tigray People's Liberation Front, were pushing "deep" into Amhara territory and hinted at possible retaliation.
Rebels from Ethiopia's war-hit Tigray region have seized Lalibela, a UNESCO World Heritage Site in the neighbouring Amhara region famed for its 12th-century rock-hewn churches, according to residents.
The development came on Thursday as a senior Amhara official told AFP the rebels, known as the Tigray People's Liberation Front (TPLF), were pushing "deep" into Amhara territory and hinted at possible retaliation.
"I believe now, enough is enough. Because the TPLF is no more in Tigray. TPLF is moving deep into Amhara territories," said Amhara deputy president Fanta Mandefro.
"We need to defend our people," he added.
The TPLF's weeks-long push beyond Tigray has drawn criticism from world leaders and, according to Ethiopian officials, displaced hundreds of thousands of civilians.
Tigray has been wracked by fighting since last November, when Prime Minister Abiy Ahmed sent troops to topple the TPLF, the regional ruling party which dominated national politics before Abiy took office in 2018.
Abiy, winner of the 2019 Nobel Peace Prize, said the move came in response to TPLF attacks on army camps.
But while Abiy promised victory would be swift, the war took a stunning turn in June when pro-TPLF forces retook the Tigray capital Mekelle and the Ethiopian army largely withdrew.
Since then the TPLF has pressed east into neighbouring Afar and south into neighbouring Amhara, where Lalibela is located.
Soldiers and militia fighters have mobilised en masse in parts of Amhara to head off the rebels' advance, but multiple residents of Lalibela told AFP on Thursday that the town fell without a fight.
"They came in the afternoon, and there was not any fighting. There were no security forces around. The TPLF forces are in the town now," one resident said.
"The TPLF just arrived in the afternoon. They were dancing and playing in the square of the city," another resident said.
"Most of the people are leaving the town to the remote areas," a third resident said, adding that he was hiding in his home with his family.
The United States urged the rebels to protect the heritage site with State Department spokesman Ned Price also renewing calls for an end to the violence.
The TPLF's push into the neighbouring regions has elicited global criticism, with the UN additionally reiterating calls for all parties to end hostilities.
Billene Seyoum, Abiy's spokeswoman, told a press conference Thursday that more than 300,000 people had been displaced by recent fighting in Amhara and Afar.
Abiy's government has long accused foreign, especially Western leaders of overlooking crimes committed by the TPLF, and Billene said Thursday the TPLF "continues to play" some foreign observers "like a ventriloquist."
"I hope that the international community at this juncture will begin to wake up and see this organisation for what it is: a terrorist organisation that has hijacked the wellbeing of the people of Tigray as a means for its vicious goals," she said.
Officials did not immediately confirm on Thursday that Lalibela was under TPLF control.
Fanta, the Amhara deputy president, said late Thursday he did not have information on the latest troop movements.
Over 200,000 newly displaced civilians
He said the region was struggling to accommodate more than 200,000 newly displaced civilians, some of whom have been forced to move multiple times to avoid combat.
"The situation is very sad, pregnant women are delivering in the rain. Babies are born in the rain showers," he said.
"It's beyond imagination to describe the current situation the displaced people are living in. It's the rainy season, the conflict is continuing, it's nonstop... The government is trying to defend and to stop TPLF but it is very difficult."
Regional spokesman Gizachew Muluneh said some civilians had been killed, though he did not give a figure.
The Amhara town of Kobo, located roughly 100 kilometres (60 miles) east of Lalibela, is also under TPLF control after days of heavy fighting, an Amhara militia fighter told AFP this week.
"The war was accompanied by heavy artillery. We were armed with Kalashnikovs but they were launching mortars and using snipers," said the militia fighter, Eskindir Molla, who has since retreated south to the town of Woldiya.
"The TPLF opened fire on four fronts, and we fought for five days," he added.
"The people who are still there [in Kobo] are begging us to go back to save them. They are currently in a desperate condition."
The TPLF has said it does not intend to expand territorial gains beyond Tigray and is instead trying to "degrade" the soldiers and militia fighters deploying north.
However it has vowed to "liberate" southern and western Tigray, parts of the region that were occupied by Amhara forces and officials in the early stages of the war.
World leaders, meanwhile, are urging the TPLF to commit to a ceasefire to facilitate aid delivery in Tigray, where the UN estimates fighting has pushed 400,000 people into famine-like conditions.
At river where Tigrayan bodies floated
From time to time, a body floating down the river separating Ethiopia’s troubled Tigray region from Sudan was a silent reminder of a war conducted in the shadows. But in recent days, the corpses became a flow.
Bloated, drained of colour from their journey, the bodies were often mutilated: genitals severed, eyes gouged, a missing limb. The Sudanese fishermen who spotted them, and the refugees from Tigray who helped pull them to shore, found many corpses’ hands bound. Some of them had been shot.
The Associated Press reported dozens of bodies floating down the Tekeze River earlier this week and saw six of the graves on Wednesday, marking the first time any reporters could reach the scene.
Doctors who saw the bodies said one was tattooed with a common name in the Tigrinya language and others had the facial markings common among Tigrayans, raising fresh alarm about atrocities in the least-known area of the Tigray war.
“They are from Tigray,” said Garey Youhanis, a Tigrayan who helped bury several bodies found on Sunday. With a piece of red cord, he demonstrated how their hands were tied behind their backs. He squatted on the rock-strewn shore, crossed himself and prayed.
The deaths are the latest massacre in a nine-month war that has killed thousands of civilians and is now spilling into other regions of Ethiopia, Africa’s second most populous country and the anchor of the often-volatile Horn of Africa.
Though Tigray forces in June reclaimed much of the region as Ethiopian and allied forces retreated, western Tigray is still controlled by authorities from Ethiopia’s neighbouring Amhara region, who have cleared out many ethnic Tigrayans while saying the land is historically theirs. Witnesses have told the AP of watching mass expulsions.
More than 60,000 Tigrayans fled to Sudan, where thousands remain in makeshift camps a short walk from the river in the hope of hearing news from those who still arrive. Some scrutinised the bodies in the river for clues, and they have asked Sudanese police and the United Nations to exhume them for autopsies.
“In the last one week, 43 bodies were buried around this river,” the surgeon from the nearby Tigray town of Humera, Tewodros Tefera, told the AP. He and other refugees believe the bodies were dumped into the river at Humera, which has seen some of the worst violence since the war began in November.
“Some had amputated limbs and legs,” Tewodros said. “There was a man which we buried yesterday, his genital area was completely severed. ... So this is the kind of trauma that we’re seeing of western Tigray.”
He told the AP they hadn’t heard of any new bodies since Tuesday, when at least seven were found. But he believes an active search along the river could reveal “many, many more,” perhaps hundreds.
Ethiopia’s government has accused the rival Tigray forces of dumping the bodies themselves for propaganda purposes. A "fake massacre,” the spokeswoman for Prime Minister Abiy, Billene Seyoum, told reporters on Thursday.