Prime Minister Abiy Ahmed on Thursday ordered Ethiopia's army to launch a "final" offensive against Tigray's dissident leaders in their regional capital Mekele, saying the deadline for their surrender had expired.

Abiy, the winner of last year's Nobel Peace Prize, late Sunday gave the Tigray People's Liberation Front (TPLF) 72 hours to lay down their arms.

Hundreds have died and over 40,000 have been displaced Hundreds have died and over 40,000 have been displaced Photo: AFP / EDUARDO SOTERAS

The ultimatum was rejected by the leaders of the region, whose forces have been fighting federal troops in the country's north for three weeks.

The violence has claimed hundreds of lives and displaced more than 40,000, with some refugees claiming Thursday that Ethiopia's army has blocked a main road to Sudan, preventing those fleeing the conflict from crossing the border.

Ethiopia's army -- which in recent days said it was advancing on Mekele with tanks -- have been directed "to conclude the third and final phase" against the TPLF, Abiy said.

Two members of the Amhara militia in Mai Kadra, where at least 600 civilians were killed, according to Rthiopia's rights watchdog Two members of the Amhara militia in Mai Kadra, where at least 600 civilians were killed, according to Rthiopia's rights watchdog Photo: AFP / EDUARDO SOTERAS

"In this final phase, great care will be given to protect innocent civilians from harm. All efforts will be made to ensure that the city of Mekele, which was built through the hard work of our people, will not be severely damaged," Abiy promised.

He said "thousands" of TPLF militia and special forces had surrendered to federal forces before the deadline lapsed.

It was not immediately clear how close the army was to the city. A communications blackout in Tigray and restrictions on reporting have made verifying claims from both sides difficult.

27-year-old Berekhti Burro is one of 700 pregnant women among the new arrivals of refugees seeking shelter in the rapidly growing tent-town of Um Raquba refugee camp in Sudan 27-year-old Berekhti Burro is one of 700 pregnant women among the new arrivals of refugees seeking shelter in the rapidly growing tent-town of Um Raquba refugee camp in Sudan Photo: AFPTV / Mujahed Sharaf AL-DEEN SATI

Ethiopia's Tigray region and its importance in national politics Ethiopia's Tigray region and its importance in national politics Photo: AFP / Nioucha ZAKAVATI

Diplomats briefed on the fighting told AFP on Wednesday that federal forces were at least 30 kilometres (18 miles) from Mekele to the north and the south.

The threatened assault and fears for Mekele's half a million inhabitants accelerated diplomatic efforts to mediate, with the UN Security Council holding its first meeting on the crisis on Tuesday.

UN Secretary General Antonio Guterres urged "the leaders of Ethiopia to do everything possible to protect civilians" as the US, EU and other international powers encouraged mediation through the African Union (AU), which is headquartered in Addis Ababa.

More than 40,000 people have crossed into eastern Sudan, where the UN says a "full-blown humanitarian crisis is unfolding More than 40,000 people have crossed into eastern Sudan, where the UN says a "full-blown humanitarian crisis is unfolding" Photo: AFP / ASHRAF SHAZLY

Rights groups have warned bombarding Mekele could constitute a war crime.

"Despite the Ethiopian military's warnings to residents, warnings alone do not absolve the government of its obligation to take constant care to protect civilians, particularly when using airpower and heavy weaponry" in congested urban areas, Human Rights Watch said.

Abiy stressed that Ethiopia's defence forces had "carefully devised" a strategy to defeat the TPLF in Mekele without harming civilians or public property.

A man reacts near a body-filled ditch outside Mai-Kadra, where 600 civilians are believed to have been massacred A man reacts near a body-filled ditch outside Mai-Kadra, where 600 civilians are believed to have been massacred Photo: AFP / EDUARDO SOTERAS

"We call on the people of Mekele and its environs to disarm, stay at home and stay away from military targets" and assist by handing over TPLF elements in their midst, Abiy said.

Abiy ordered troops into Tigray on November 4 following alleged attacks by TPLF forces on federal military camps in the region.

He has resisted appeals for talks. His government signalled it would meet the AU envoys "as a matter of respect", but flatly refused to negotiate.

As international pressure mounted this week, Abiy issued a strongly-worded statement rejecting outside "interference" in what he labelled an internal "law enforcement" operation.

Since the fighting began, rockets have fallen on the Eritrean capital Asmara and Ethiopian cities outside Tigray, spurring fears the conflict could destabilise the wider Horn of Africa region.

Hundreds have reportedly been killed, although an accurate figure is not known. Ethiopia's rights watchdog this week said at least 600 civilians were massacred in the Tigrayan town of Mai-Kadra alone.

The UN, in its latest crisis report, said shortages of cash and fuel were "very critical" in Tigray and humanitarians were struggling to meet needs.

Abiy committed Thursday to opening a humanitarian access route into Tigray and working with the UN and other aid agencies to help those in need.

More than 40,000 people have crossed into eastern Sudan, where the UN says a "full-blown humanitarian crisis is unfolding" in one of the country's poorest regions.

"The numbers are way above the state's capabilities," Soliman Ali, the governor of the border state of Gedaref, told AFP.

The number of refugees arriving in Sudan has fallen sharply in the last week. Refugees arriving in eastern Sudan on Thursday accused Ethiopia's army of blocking a road at Humera near the border.

"Those seeking to reach Sudan must avoid the main road and pass through fields without being seen by soldiers," said Tesfai Burhano, who had just arrived at the Lugdi crossing point.

The TPLF led the overthrow of Mengistu Hailemaria, leader of Ethiopia's military Derg regime, in 1991 and dominated the country's politics until Abiy became prime minister in 2018.