The ministers said in a joint statement that they had "agreed to embark on consultations at the technical and political levels" and that such talks would be in "a spirit of brotherly relations and mutual understanding." Sudan also will participate in these talks.
Mohamed Amr, Egypt's foreign minister, arrived in Ethiopia on Sunday for talks with Tedros Adhanom, his Ethiopian counterpart, amid a sharp exchange of words between their governments over the dam.
"I always said that no Nile, no Egypt. And I am sure our brothers in Ethiopia understand and appreciate that and will always keep the Nile flowing to Egypt," Amr told a news conference in the Ethiopian capital, Addis Ababa.
Ethiopia's growing economy frequently suffers from power cuts and needs more electrical capacity, but Nile-dependent Egypt fears the project will diminish its share of Nile River waters.
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Ethiopia last month started to divert Nile waters to make way for its massive USD 4.2 billion hydro-electric dam dubbed the Grand Ethiopian Renaissance Dam, sparking concerns in Egypt.
Ethiopia's parliament on Thursday unanimously ratified a new accord that replaces colonial-era deals that awarded Egypt veto powers over Nile projects.
Ethiopia's leaders say work on the dam will not stop even as consultations proceed. They say the findings of an experts' panel, which includes four international experts, show the dam will not significantly affect water flow to both Egypt and Sudan.