That caused global alarm as rights groups said such wording could violate worldwide law and put civilians in further danger.
The war has spread to Eritrea, where the Tigrayans have fired rockets, and also affected Somalia where Ethiopia has disarmed several hundred Tigrayans in a peacekeeping force fighting Al Qaeda-linked militants. On Thursday, however, the delegation was unable to meet Mr. Abiy.
Abiy, the victor of last year's Nobel Prize, late Sunday gave the Tigray People's Liberation Front (TPLF) 72 hours to surrender - an ultimatum rejected by the leader of the dissident northern region, whose forces have been fighting Ethiopian troops for three weeks.
He said the military would try not to harm civilians and urged people in the city to stay at home.
He said "thousands" of TPLF militia and special forces had surrendered to federal troops before the deadline lapsed. With communications shut down and media barred from the region, it was hard to know if the assault had begun.
Abiy, who won last year's Nobel Peace Prize for ending a two-decade standoff with Eritrea, has said he will receive them but not talk with TPLF heads until they are defeated or give up.
He urged the people of Mekele to "stay at home and stay away from military targets".
In the "final phase" of the military offensive that PM Abiy launched following the expiry of the 72-hour ultimatum, he spoke of a military strategy in which top personnel of the TPLF would be brought to justice without harming civilians or properties in and around Mekelle.
The commission says the group stabbed, bludgeoned and burned to death non-Tigrayan residents of the town of Mai-Kadra with the collusion of local forces.
On Tuesday, Human Rights Watch said both sides must avoid putting civilians in danger, adding the government's warning did not absolve it "of its duty to take constant care to protect civilians when carrying out military operations in urban areas".
The conflict is rooted in longstanding tension between Ethiopia's central government and the TPLF, which was the dominant political force in the whole country until Mr Abiy came to power in 2018 and introduced a series of far-reaching reforms.
The EU's foreign policy chief Josep Borrell on Tuesday discussed the worsening humanitarian crisis with Ethiopia's foreign minister, and warned the fighting was already destabilising the wider region.
Ethiopia has described the fighting as an internal law enforcement matter, a position Prime Minister Abiy Ahmed reiterated in a statement on Wednesday.
Ethiopian Prime Minister Abiy Ahmed on Wednesday rejected more calls for dialogue over the Tigray crisis, terming continued pressure to de-escalate as outside interference.
Although Ethiopia is ultimately responsible for the conduct and movement of the roughly 2,000 troops it had in South Sudan, the statement said, discrimination due to ethnicity could violate worldwide law.
Other people are frantically moving within the Tigray region from one district to another and "living within church compounds, streets, schools, health centres", the statement warned, and it pleaded for a safe corridor to ship in aid as food runs out.
Most of the 600,000 people in Tigray who rely on monthly food assistance have not received their November rations, and a further 250,000 people who are "among the poorest" have not received their normal monthly support payments, the report said.
