Ethiopian Prime Minister Abiy Ahmed said Tuesday military operations in the northern Tigray region would enter a "final" phase, as global pressure mounted to bring the two-week-old conflict to a swift end.

Fresh air strikes hit the regional capital of Mekele on Monday as East African leaders called for an end to the conflict and for dialogue, which Ethiopia has so far resisted.

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

The fighting has left hundreds dead and prompted around 25,000 Ethiopians to flee across the border into Sudan, with many more refugees expected.

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.

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 c