Ethiopia's prime minister warned on Tuesday that a deadline for rebel northern forces to lay down arms had expired, paving the way for a final push on the Tigray region's capital in a two-week conflict destabilising the Horn of Africa.

"The three-day ultimatum given to Tigray Special Forces and the militia to surrender ... has ended today," Prime Minister Abiy Ahmed said on Facebook. "The final critical act of law enforcement will be done in the coming days."

Africa's youngest leader and the 2019 Nobel Peace Prize winner, Abiy launched air strikes and a ground offensive on Nov. 4 after accusing the local ruling party, the Tigray People's Liberation Front (TPLF), of armed mutiny against his authority.

Tigrayan leaders say Abiy, 44, who comes from the largest ethnic group the Oromo, has persecuted and purged them from government and security positions since taking office in 2018.

Tigrayan forces fired rockets into the neighbouring nation of Eritrea this weekend, widening a conflict which has already killed hundreds - one diplomatic source said thousands - of combatants and civilians, and sent 25,000 refugees into Sudan.

With communications mainly down and media barred, Reuters could not independently verify assertions made by any side.

Abiy's warning came after his forces struck unspecified TPLF targets outside the Tigray capital Mekelle, a government emergency task-force said.

"The Ethiopian National Defense Forces indeed undertook precision-led and surgical air operations outside of Mekelle city," it said, adding that civilian areas were avoided.

There was no immediate response from Tigray's leaders, though they have accused federal forces of knocking out a dam and a sugar factory as well as "mercilessly" attacking people in the region of more than 5 million.

'HEAVIER FIGHTING LIKELY'

Tigrayan forces might seek to dig in as the military advances into the more mountainous terrain towards Mekelle, said Matt Bryden, founder of Nairobi-based regional think-tank Sahan.

"I would guess as they (the Ethiopian army) enter the highlands, heavier fighting is likely to start," he said.

With hundreds of thousands of Tigrayans dependent on food aid even before the conflict, suffering is worsening fast even as United Nations and aid agency staff are scaling back for security reasons.

A convoy of four buses and several cars, carrying about 400 foreigners from Mekelle, was expected to arrive in the capital Addis Ababa on Wednesday, five diplomatic sources said.

Another convoy of about 200 people, mainly workers for international organisations, reached the capital on Monday.

The United Nations and governments around Europe and Africa are pressing for talks, but Abiy has resisted, saying he will only negotiate when rule of law is restored in Tigray.

On Monday, Abiy's foreign minister went to Uganda and Kenya, while a Nigerian former president flew to Addis Ababa. Diplomats described a growing push for negotiations, but Ethiopia said it was simply explaining an internal conflict to outsiders.

Ethiopia, Africa's second-most populous country, has long been a diplomatic and economic heavyweight and Western ally in a region of conflict, poverty and Islamist militancy.

Abiy has appealed for refugees to come home as his government promises the war will end quickly, though experts fear a protracted conflict given considerable military muscle on both sides.

The fighting could jeopardise the recent opening up of Ethiopia's economy, stir ethnic bloodshed elsewhere around the vast nation of 115 million people, and tarnish the reputation of Abiy who won his Nobel for pursuing peace with Eritrea.

The federal forces comprise around 140,000 personnel and are battle-hardened from fighting Somali militants, rebels in border regions and Eritrea in the past. But many senior officers were Tigrayan, much powerful weaponry is there, and the TPLF has seized the powerful Northern Command's headquarters in Mekelle.

The TPLF itself is a formidable rival also with a proud history: it spearheaded the rebel march to Addis Ababa that ousted a Marxist dictatorship in 1991 and bore the brunt of the 1998-2000 war with Eritrea that killed hundreds of thousands.