Rebels from Ethiopia's war-hit Tigray region have seized Lalibela, a UNESCO World Heritage Site in the neighbouring Amhara region famous for its 12th-century stone churches.

The development came as a senior Amhara official said the rebels, known as the Tigray People's Liberation Front (TPLF), were pushing 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 hit 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 he took office in 2018.

The rock-hewn monolithic church of Bet Giyorgis in Lalibela, Ethiopia (file photo)

Mr Abiy, winner of the 2019 Nobel Peace Prize, said the move came in response to TPLF attacks on army camps.

But while Mr Abiy promised victory would be swift, the war took a turn in June when pro-TPLF forces retook the Tigray capital Mekele 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 said 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.

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.