Ethiopian Prime Minister Abiy Ahmed says the war in the northern Tigray region "will end and peace will prevail".
He made the remarks on Thursday when he inaugurated a talent development centre in Oromia regional state.
"The situation in northern Ethiopia will come to an end, peace will prevail. We will not continue fighting forever. I believe that in a short period of time, we will stand with our Tigrayan brothers for peace and development," Mr Abiy said.
He urged Ethiopians to work together for the country's prosperity and not to be divided along ethnic and religious lines.
On Thursday, the Ethiopian government accepted an invitation by the African Union to participate in peace talks to be held on 24 October in South Africa to end the war that has killed an unspecified number of people and displaced millions.
It came on the same day Tigrayan rebels accused Ethiopian and Eritrean forces of killing seven youths in a town that was captured by the federal army on Tuesday.
- Intense fighting -
The resumption of fighting on 24 August in northern Ethiopia put an end to a five-month truce and the meagre hopes for talks that it had raised.
The international community has been concerned in recent days about the recent intensification of fighting in Tigray, which is being pinched by Ethiopian federal forces, supported in the north by the army of Eritrea - the country that borders Tigray in the north - and in the south by troops from neighbouring Ethiopian regions.
Ethiopian and Eritrean forces seized Shire, one of the main towns in Tigray, which had a population of about 100,000 before the war and was home to many people displaced by the conflict, on Monday after several days of bombing.
A humanitarian source who requested anonymity said intense fighting was taking place on Friday in Selekelka, halfway between Shire and Aksum, referring to a "push" by Ethiopian and Eritrean forces towards this other important town in Tigray, which is home to a World Heritage site.
Price said the US special envoy for the Horn of Africa, Mike Hammer, had been in Addis Ababa for several days "supporting the AU's efforts to launch the talks" which Washington "wants to see begin as soon as possible".
Mr Hammer "is in constant contact with the parties involved, including those preparing to participate in the mediation, particularly Kenya and South Africa," the US spokesman added.
The AU recently set up a mediation "troika" led by Obasanjo, assisted by former Kenyan President Uhuru Kenyatta and former South African Vice President Phumzile Mlambo-Ngcuka.
In a telephone exchange on Wednesday with the UN secretary-general, US Secretary of State Antony Blinken said he was "deeply concerned" about the "risk of mass atrocities" in northern Ethiopia.
On Monday, Mr Guterres said the situation in Ethiopia was getting "out of control".
The toll of this deadly war, which is taking place behind closed doors as journalists are denied access to the region, is unknown. But it has displaced more than two million people and plunged hundreds of thousands of Ethiopians into near-starvation conditions, according to the UN.