Since 2014, Egypt, Ethiopia, and Sudan have entered into negotiations on the building of the dam to avoid any possible threats on the Nile downstream countries [Egypt and Sudan].
Egyptian Presidential Spokesperson Bassam Radi in a statement that during a phone call, the two leaders tackled Egypt's request to the Security Council to intervene to reach a fair and balanced agreement that takes into account the interests of all parties.
There was no immediate comment from Ethiopia on the agreement, beyond a tweet from Prime Minister Abiy Ahmed that described an African Union (AU) summit discussion about the dam as "fruitful".
On Friday, the three countries agreed to form a committee of legal and technical experts to draft a final binding deal, and to "refrain from taking any unilateral measures, including the filling of the dam, before the agreement is reached", the Egyptian presidency said in a statement.
Addis Ababa has been vocal about its plans to start filling the reservoir in July, and Abiy faces intense domestic political pressure to stick to that timeline.
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.
FILE - This satellite image taken Thursday, May 28, 2020, shows the Grand Ethiopian Renaissance Dam on the Blue Nile river in the Benishangul-Gumuz region of Ethiopia. Sudan, which also depends on the Nile for water, has played a key role in bringing the two sides together after the collapse of US-mediated talks in February.
African Union Commission Chairman Moussa Faki Mahamat said the countries "agreed to an AU-led process to resolve outstanding issues", without elaborating.
Egypt previously made a decision to request the United Nations Security Council's intervention in the dispute on Ethiopia's massive dam, after Egypt had said several times that the two countries have reached a deadlock.
The announcement came after an emergency African Union online summit of leaders of the three countries chaired by South African president Cyril Ramaphosa.
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.
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".
Diplomatic sources said this week that the UN Security Council planned to meet Monday to discuss objections to the dam raised by Egypt and Sudan.
The dam could be the centrepiece in Ethiopia's bid to become Africa's biggest power exporter, but has sparked concerns in Cairo that Egypt's already scarce supplies of Nile waters, on which its population in excess of 100 million people is practically entirely dependent, would be further restricted.