"It is in this period that the three countries have agreed to reach a final agreement on few pending matters", a statement from the Ethiopian prime minister's office said.
"Ethiopia is scheduled to begin filling the GERD within the next two weeks, during which the remaining construction work will continue".
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.
More than 90% of issues in the tripartite negotiations on the giant Nile dam between Egypt, Ethiopia and Sudan have been resolved, the African Union Commission Chair Moussa Faki Mahamat said in a statement on Saturday.More news: Cirque du Soleil files for creditor protection in Canada
They also signal an intention to solve the issue without foreign intervention.
Early Saturday, Seleshi Bekele, Ethiopia's water and energy minister, confirmed that the countries had decided during an African Union summit to restart stalled negotiations and finalize an agreement over the contentious megaproject within two to three weeks, with support from the African Union.
Responding to Egypt's decision to take the issue of the GERD to the UN Security Council, Ethiopian Foreign Minister Gedu Andargachew in a June 22 letter said Egypt's insistence on the "historical rights and current use" has made it hard to reach a settlement on the dispute.
Sisi stressed that Egypt holds a honest desire to reach a fair and balanced agreement on the GERD that enables Ethiopia to achieve its desired economic development and increase its capacity to generate electricity, while taking into account Egypt and Sudan's water rights as well.
The 1959 agreement allocated almost 90 per cent of the Nile waters to Egypt and Sudan, with Egypt taking 55.5 billion cubic meters annually while Sudan was allocated 18.5 billion cubic meters per year.More news: Researchers identify drugs that may block cell to cell transmission of coronavirus
The African Union is mediating and Ethiopia's government says the parties could finalise an agreement within two to three weeks.
The summit sent a letter to the UN Security Council to take the matter into consideration during its session on Monday to discuss the GERD issue.
Both Egypt and Sudan have appealed to the U.N. Security Council to intervene in the years-long dispute and help the countries avert a crisis.
Cairo had appealed to the United Nations council in a last-ditch diplomatic move aimed at stopping Ethiopia from filling the dam.
The Egypt-Ethiopia dispute now raises the question as to why most Nile Basin countries have not ratified the CFA in order to make the agreement take effect. Both Egypt and Ethiopia have hinted at military steps to protect their interests, and experts fear a breakdown in talks could lead to open conflict. Construction of the Dam started in April 2011.More news: Coronavirus Lockdown: Europe Reopens Borders to 15 Countries, US Excluded from List