During a visit to South Africa on Sunday, Abiy Ahmed said President Cyril Ramaphosa as the incoming chair of the African Union could play an important role in ensuring a peaceful resolution is found.
Talks last week among Ethiopia, Egypt and Sudan failed to reach agreement on technical issues including the filling of the $4.6 billion Ethiopian Renaissance Dam, which is around 70% complete.
Egypt has said filling the dam's reservoir too quickly could significantly reduce the amount of Nile water available to its people and agriculture. Ethiopia says the dam is needed for development in one of Africa's fastest-growing economies.
Last week Ethiopia said Egypt asked to extend the time it takes to fill the dam from 12 years to 21 years. Ethiopia called that "not acceptable" and plans to start filling the dam in July at the start of the rainy season.
Egypt later said Ethiopia's government failed to prove it would take all necessary precautions to ensure that the dam will not affect Egypt's water supply, especially in times of drought.
Water and energy ministers of Ethiopia, Egypt and Sudan are expected to meet again Monday in Washington to report on their progress. The U.S. and World Bank are observers to the talks after Egyptian President Abdel Fattah el-Sissi last year pleaded to the U.S. and the international community to mediate a solution.
"Ethiopia always believes in a win-win approach with Egypt and Sudan. Our kind request is that Ramaphosa ... as he is a good friend of Ethiopia and Egypt, also as the incoming African Union chair, he can make a discussion between both parties for us to solve the issue peacefully," Abiy said Sunday.
He called it crucial that a peaceful solution be found and said he is sure Ramaphosa will "play a significant role" in negotiations.
The South African leader confirmed that he had already raised the matter with the Egyptian president.
"The Nile river is important to both countries and there must be a way in which both their interests can be addressed. There must be a way in which a solution can be found," Ramaphosa said.
Ethiopia and South Africa signed several trade agreements in health, tourism and telecommunications during Abiy's visit.
Ramaphosa also gave assurances to the Ethiopian prime minister that his country would protect Ethiopians living in South Africa from the xenophobic attacks that break out in South Africa. Last year, foreign businesses were targeted by locals in Johannesburg and the capital, Pretoria.