The territorial dispute between Ethiopia's northern Amhara and Tigray regions will be settled through a referendum, the government says.
The row has threatened to disrupt the fragile peace following the end of the civil war in Tigray a year ago.
Tigray controlled the fertile lands before Amhara forces seized them in 2020 during the conflict.
Rights groups have accused those forces of carrying out ethnic cleansing in the disputed areas.
The allegations were dismissed by Amhara's regional government.
The disputed areas, near Ethiopia's border with Sudan, were a key flashpoint in the two-year conflict between the Tigray People's Liberation Front (TPLF) and the federal government.
The war ended after a peace agreement was signed last November in South Africa.
Many of the one million displaced people, who remain sheltered in makeshift camps throughout Tigray, are reported to have fled the contested areas.
The Amhara administration says the territory was forcibly annexed by Tigray in the 1990s when the TPLF was the dominant political force in Ethiopia.
In a lengthy report last year, rights groups Amnesty International and Human Rights Watch said evidence collected through interviews showed that the disputed areas had been the site of some of the worst atrocities committed during the conflict and were been largely ignored.
The African Union envoy, former Nigerian President Olusegun Obasanjo, has said around 600,000 people died during the conflict overall. Researchers put the hundreds of thousands of civilian deaths down to fighting, starvation and lack of health care.
In Monday's statement evaluating the year since the peace deal, the government said the displaced people would be returned and the federal military would assume responsibility for local security.
The federal authorities say they have "taken a position on the fate of the disputed areas to find a solution mutually beneficial to all sides".
"A direction has been put in place for a referendum to be held in accordance with the constitution," the government's communication service said.
It did not say when the referendum would be held.
The statement - released in Amharic and English - also hailed progress made in the past 12 months including the formation of an interim administration in Tigray. But it accused the administration of "dragging its feet" over fully implementing the peace deal.
It also suggested the administration was still keeping combatants despite agreeing to disarm.
Tigrayan forces have handed over their heavy weapons but it is believed that small and light arms have not been given up. The TPLF, in a statement last week, said the ceasefire had not been fully implemented because large numbers of people were still displaced.
This comes amid heavy fighting between Ethiopian federal troops and local militias across large parts of the Amhara region.
The fighting broke out in April after the federal government's directive to disarm regional forces and armed groups.
Fighters from the Fano militia say they have captured several towns in Ethiopia's second-biggest region. The federal government has not yet commented on the claims.
In August, the militias entered several of the region's main cities, temporarily taking control of an airport in the historic town of Lalibela before they were pushed out by the army.
The Ethiopian Human Rights Commission (EHRC) has accused federal forces of human rights violations in the clashes with Fano rebels.
The Ethiopian government denied the EHRC report, terming it "unbalanced".
Western countries including Britain and the US have called for a dialogue.