The UN said Tuesday a full-blown humanitarian crisis was unfolding in northern Ethiopia, where thousands of people each day are fleeing the conflict in the Tigray region.

As international pressure mounted over his campaign against the dissident region, Ethiopian Prime Minister Abiy Ahmed declared operations were entering a "final" phase, and his government confirmed fresh air strikes near the Tigray capital, Mekele. 

Abiy, last year's Nobel Peace Prize winner, announced a military campaign on November 4, saying it came in response to attacks by the local ruling party, the Tigray People's Liberation Front (TPLF), on federal military camps.

The United Nations refugee agency said around 27,000 Ethiopians have fled across the border into Sudan -- a figure now rising by around 4,000 people each day. 

"A full-scale humanitarian crisis is unfolding," spokesman Babar Baloch told a virtual press briefing from Geneva.

"Refugees fleeing the fighting continue to arrive exhausted from the long trek to safety, with few belongings." 

Those arriving in Sudan recounted terrifying scenes of artillery barrages and massacres.

"I saw bodies dismembered by the explosions," said Ganet Gazerdier, 75, whose home was destroyed in the town of Humera, and finds herself at a refugee camp in eastern Sudan.

"Other bodies were rotting, lying on the road, murdered with a knife", she added.

Final throes of death

On Friday Abiy declared the TPLF was "in the final throes of death" and gave troops in the region three days to "rise up" and side with the national army.

In a Facebook post Tuesday morning, he said their time was up.

"The three-day deadline for the Tigray regional special forces and militia to hand themselves over to national defence forces instead of being a tool for the greedy junta has expired. Those Tigray special forces and militia who used the three-day deadline are appreciated," he said. 

"Since the deadline has been completed, in the coming days the final law enforcement activities will be done."

A communications blackout in Tigray has made it difficult to assess how the fighting is going or verify a death toll that could be in the hundreds. 

Federal forces claim to control Tigray's western zone, where fighting has been heavy, and over the weekend said they had seized the town of Alamata, 180 kilometres (110 miles) south of the regional capital, Mekele.

But Tigrayan leader Debretsion Gebremichael told AFP Tuesday that "the government and people of Tigray" would hold their ground.

"This campaign cannot be finished. As long as the army of the invaders is in our land, the fight will continue. They cannot keep us silent by military force," he said. 

Abiy has resisted calls by world leaders to cease hostilities and accept mediation.

On Monday, his deputy prime minister Demeke Mekonnen flew to Uganda and then to Kenya to meet with the presidents of the regional heavyweights.

"A war in Ethiopia would give the entire continent a bad image," Ugandan President Yoweri Museveni wrote on Twitter after meeting Demeke.

"There should be negotiations and the conflict stopped, lest it leads to unnecessary loss of lives and cripples the economy."

But Museveni later deleted the tweet, and an Ethiopian official said Demeke made clear negotiations were not an immediate possibility.

Kenya's President Uhuru Kenyatta later called for a "peaceful" resolution of the crisis.

Abiy's government has said there can be no mediation until Tigray's leaders have been disarmed and brought to court.  

The TPLF dominated Ethiopian politics for three decades before Abiy came to power in 2018, and a bitter feud has grown as they have been sidelined from politics, becoming ever more defiant towards the central government.

Spreading conflict 

A government statement on Tuesday said the army on Monday had carried out "precision led and surgical air operations outside of Mekele city based on information received of specific critical TPLF targets."

Debretsion said there were civilian casualties, which the government denied.

A resident of Mekele told AFP there was a low-flying warplane over the city Monday that was "very scary, very loud" and that at least one civilian died in a strike not far from a university campus.

Details on the strike and any casualties could not be verified.

In recent days the TPLF has fired rockets on airports in Ethiopia's Amhara region, south of Tigray, and in the capital of neighbouring Eritrea.

The strikes on Asmara in particular have reinforced fears Ethiopia's conflict could draw in the wider Horn of Africa region.