In the statement on Saturday, Ahmed mentioned that the River Nile and the GERD project are African issues that should be discussed "under the African umbrella to find African solutions".
Ethiopia has banked its hopes of development on the GERD and has said it has the potential to lift millions of Ethiopians out of poverty.
African Union Commission Chairman Moussa Faki Mahamat said the countries "agreed to an AU-led process to resolve outstanding issues", without elaborating.
This follows a video conference summit organized by the African Union (AU) between Egyptian President Abdel Fattah al-Sisi, Sudanese Prime Minister Abdalla Hamdok, and Ethiopian Prime Minister Abiy Ahmed with the participation of South African President and current AU head Cyril Ramaphosa, Kenyan President Uhuru Kenyatta, the President of Mali Ibrahim Abu Bakr Keita, and Congo President Felix Tshisekedi.
Responding to Egypt's decision to take the issue of the GERD to the UN Security Council, Ethiopian Foreign Minister Gedu Andargachew in a June 22 letter said Egypt's insistence on the "historical rights and current use" has made it hard to reach a settlement on the dispute.
The technical committee will try to strike a deal within two weeks as suggested by Ethiopia, his office said.
Leaders of Sudan, Ethiopia and Egypt said they were hopeful that the African Union could help them broker a deal to end a decade-long dispute over water supplies within two or three weeks.
A technical and legal committee from Egypt, Sudan, Ethiopia, and members of the AU's Assembly Bureau, will meet to formulate a legal agreement on the GERD's filling and operation.
Ethiopia says it will take three to seven years to fill the dam reservoir with 4.9 billion cubic meters of water for generation of electricity, while Egypt says it will affect the natural flow of the Blue Nile that provides it with 87 per cent of its water and has been pushing for gradual filling of between seven and 10 years to guarantee its annual share.
Addis Ababa followed suit complaining about Cairo, while Khartoum expressed its concern to the United Nations about Ethiopia unilaterally filling without a comprehensive deal being inked first.
Egypt, which views the hydroelectric barrage as an existential threat, appealed last week to the UN Security Council to intervene in the dispute.
The summit sent a letter to the UN Security Council to take the matter into consideration during its session on Monday to discuss the GERD issue.
Over the past few years, tripartite talks on the rules of filling and operating the Ethiopian grand hydropower dam, including those hosted by Washington, have been fruitless. Both Egypt and Ethiopia have hinted at military steps to protect their interests, and experts fear a breakdown in talks could lead to open conflict.
This June 2013 photo shows construction work at the site of the planned Grand Ethiopian Renaissance Dam near Assosa in the Benishangul-Gumuz region of Ethiopia, near Sudan, some 500 miles from the capital, Addis Ababa.