Abiy traveled to Egypt from Uganda where he received "The Pearl of Africa Grand Medal" Award from Ugandan President Yoweri museveni on Heroes, a national holiday in the country, "for his reconciliatory leadership in achieving peace & stability in Ethiopia & for extending Olive Branch to #Eritrea", as tweeted by his chief of staff Fitsum Arega. But at a press conferee in Cairo, Ethiopian Prime Minister Abiy Ahmed and Egyptian President Abdel Fattah al-Sisi signaled they had made a breakthrough.
He said Egypt had also promised to help locate the bodies of 38 Ethiopians killed by the Islamic State group in Libya in 2015.
Egypt has lately been concerned about the effect that an Ethiopian dam being built on the Nile river would have on water flowing to its fields downstream.
The dam is expected to reduce Egypt's share of Nile waters, further limiting the country's already scarce water resources.
Ethiopia's Prime Minister arrived in Cairo on Saturday for a two-day visit, his first since he assumed office in April.
Ethiopia and Egypt have been trading war of words sometime back after Egyptian president ranted "Nile is a matter of life and death for Egypt" - connoting that it is a red line.
The two countries have been trying for months to settle a dispute over the dam Addis Ababa is building on the Nile River that Cairo fears will threaten its water supplies. Ethiopia, which has roughly same population size, says the dam is essential for its economic development.
The $4.8bn dam is now 63% finished, and Ethiopia hopes to become a key energy hub in Africa upon its completion.
"Cairo's weak hand and inability to gain sufficient leverage over Addis Ababa will force it to coordinate dam operations if it wishes to have input on future Nile River projects", it said.
Past Egyptian leaders have threatened military action if there was any attempt to dam the Nile.
Ahmed, speaking in his native Amharic language, said Ethiopia was committed to ensuring Egypt's share of Nile water.