The rebels say the move into new territory is meant to preempt an Ethiopia government blockade that has hindered access to humanitarian aid.
Rebel forces from Ethiopia's war-torn Tigray have rebuffed US calls to leave neighbouring regions, one day after they seized famed UNESCO heritage site Lalibela, the latest turn in the nine-month conflict.
"Nothing of the sort is going to happen unless the blockade is lifted," said Getachew Reda, spokesman for the Tigray People's Liberation Front (TPLF) on Friday, referring to restrictions on humanitarian access.
Northern Ethiopia has been wracked by fighting since last November, when Prime Minister Abiy Ahmed sent troops to topple the TPLF, the then-ruling party of Tigray, which dominated national politics for nearly three decades before Abiy took office in 2018.
The move came in response to TPLF attacks on army camps, Abiy said.
But while Abiy promised victory would be swift, the war took a stunning turn in June when pro-TPLF forces recaptured the Tigray capital Mekele and the Ethiopian army largely withdrew.
Since then the TPLF has pushed east into the neighbouring Afar region and south into Amhara.
Top US officials including US aid chief Samantha Power, who visited Ethiopia this week, have called on the TPLF to withdraw and for all sides to cease hostilities and focus instead on addressing the humanitarian "catastrophe" in Tigray.
On Thursday, TPLF fighters entered Lalibela without a fight, as security forces withdrew ahead of their advance, residents said.
The move prompted Amhara's government to warn that the TPLF was pressing "deep" into Amhara territory and to hint at possible retaliation.
TPLF spokesman Getachew said the push into Lalibela was part of a bid to secure roads in northern Amhara and prevent pro-government forces from regrouping.
"You see, we are under siege. We are under blockage. Anything that Abiy is going to use to maintain its chokehold on our people, we'll make sure it doesn't pose a serious problem," he said.
Lalibela is home to 12th-century rock-hewn churches that in peacetime are a major tourist draw, as well as an airport.
The UN says fighting in Tigray has pushed 400,000 people into famine-like conditions, and estimates that more than 100,000 children could suffer from life-threatening acute malnutrition in the next 12 months.
The TPLF accuses Abiy's government of blocking aid to Tigray, and top humanitarian officials continue to decry bureaucratic and other hurdles hindering access.
The government says a unilateral ceasefire it announced in late June was intended to allow aid in, and that the TPLF's subsequent offensive undermines that effort.
Bodies by the river
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 are turning up in a regular flow.
Bloated, drained of color from their journey, the bodies were often mutilated: genitals severed, eyes gouged, a missing limb.
The Associated Press reported dozens of bodies floating down the Tekeze River earlier this week and saw six of the graves on Wednesday.
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.
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.
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.
“In the last one week, 43 bodies were buried around this river,” the surgeon from the nearby Tigray town of Humera, Tewodros Tefera, said.
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.
Ethiopia’s government has accused the rival Tigray forces of dumping the bodies themselves for propaganda purposes.
The bodies in the river brought new fears of ethnic cleansing, or the forcing of a population from a region through expulsions and other violence.
“We are deeply concerned by the latest developments,” the UN refugee agency in Sudan said on Thursday.
It confirmed seeing one of the bodies pulled from the river along with “what appear to be several fresh graves.” It said it was unable to confirm the identities of the dead or how they died.