Egyptian President Abdul Fattah al-Sisi and Ethiopian Prime Minister Abiy Ahmed stressed on Friday the need to overcome any obstacles related to negotiations over the Renaissance Dam.
In a telephone call, they hoped to reach an agreement that meets the aspirations of the Nile basin countries: Egypt, Ethiopia and Sudan, in line with the declaration of principles between them, said the Egyptian presidency.
Egypt and Ethiopia are locked in a dispute over water shares related to the construction of the dam.
Last week, irrigation ministers from the three key Nile Basin countries wrapped up a two-day meeting in Sudan's capital without resolving differences over Ethiopia's soon-to-be-finished Blue Nile dam, with Egypt calling for international mediation to help reach a "fair and balanced" agreement.
Sudan Irrigation Minister Yasser Abbas told reporters in Khartoum that progress was made but differences on filling the giant reservoir and operating rules of the Grand Ethiopian Renaissance Dam remain unsettled.
Egypt's Irrigation Ministry, meanwhile, said in a statement after the meeting that talks have stalemated, claiming Ethiopia rejected "all proposals that ... avoid causing substantial damage to Egypt."
"Ethiopia ... offered a new proposal that contradicts previously agreed principles governing the filling and operating process," said Muhammed el-Sebai, spokesman of the ministry.
He said Egypt has called for international mediation "to help reach a fair and balanced agreement that protect the three countries' rights."
Sisi said Egypt would "continue to take necessary measures at the political level and in accordance with international law to protect its rights" in Nile waters.
Despite the ongoing differences, Sisi congratulated the Ethiopian premier on Friday for winning the Nobel Peace Prize.
"It is a new victory for our black continent which always aspires for peace and pursues stability and development," Sisi wrote on his official Facebook page shortly after the prize was announced on Friday.
"I hope that our constructive efforts aiming at ending all conflicts and differences in Africa will continue thanks to the will of our great sons and people."
Egypt relies on the Nile for up to 90% of its fresh water, and fears the dam, which is being built in Ethiopia close to the border with Sudan, will restrict already scarce supplies.