But Egypt, with a population of around the same size, fears that the process of filling the reservoir behind the dam could slice into its share of the river, with catastrophic consequences. Pro-government media have cast it as a national security threat that could warrant military action.
Speaking at the U.N. last month, Egyptian President Abdel-Fattah el-Sissi said he would "never" allow Ethiopia to impose a "de facto situation" by filling the dam without an agreement.
"While we acknowledge Ethiopia's right to development, the water of the Nile is a question of life, a matter of existence to Egypt," he said.
Ethiopian President Sahle-Work Zewude, also speaking at the U.N. General Assembly, said her country believes "the use of the river should be (decided) according to international law and fair and equitable use of natural resources."
Egypt has been holding talks for years with Ethiopia and Sudan, upstream countries that have long complained about Cairo's overwhelming share of the river, which is enshrined in treaties dating back to the British colonial era. Those talks came to an acrimonious halt earlier this month, the third time they have broken down since 2014.
"We are fed up with Ethiopian procrastination. We will not spend our lifetime in useless talks," an Egyptian official told The Associated Press. "All options are on the table, but we prefer dialogue and political means."
Egypt has reached out to the United States, Russia, China and Europe, apparently hoping to reach a better deal through international mediation. The White House said earlier this month it supports talks to reach a sustainable agreement while "respecting each other's Nile water equities."
Egypt said it has accepted an invitation from the U.S. to meet in Washington with the foreign ministers of Ethiopia and Sudan to break the deadlock.
Mohamed el-Molla, an Egyptian Foreign Ministry official, said Cairo would take the dispute to the U.N. Security Council if the Ethiopians refuse international mediation.
That has angered Ethiopia, which wants to resolve the dispute through the tripartite talks.
An Ethiopian official said the packages offered by Cairo so far "were deliberately prepared to be unacceptable for Ethiopia."
"Now they are saying Ethiopia has rejected the offer, and calling for a third-party intervention," the official added. Both the Ethiopian and the Egyptian official spoke on condition of anonymity because they were not authorized to discuss the talks with the media.
The main dispute is centered on the filling of the dam's 74-billion-cubic-meter reservoir. Ethiopia wants to fill it as soon as possible so it can generate over 6,400 Megawatts, a massive boost to the current production of 4,000 Megawatts.
That has the potential to sharply reduce the flow of the Blue Nile, the main tributary to the river, which is fed by annual rainfall in the Ethiopian highlands. If the filling takes place during one of the region's periodic droughts, its downstream impact could be even more severe.
Egypt has proposed no less than seven years for filling the reservoir, and for Ethiopia to adjust the pace according to rainfall, said an Egyptian Irrigation Ministry official who is a member of its negotiation team. The official also was not authorized to discuss the talks publicly and so spoke on condition of anonymity.
The Nile supplies more than 90% of Egypt's freshwater. Egyptians already have one of the lowest per capita shares of water in the world, at around 570 cubic meters per year, compared to a global average of 1,000. Ethiopians however have an average of 125 cubic meters per year.
Egypt wants to guarantee a minimum annual release of 40 billion cubic meters of water from the Blue Nile. The irrigation official said anything less could affect Egypt's own massive Aswan High Dam, with dire economic consequences.
"It could put millions of farmers out of work. We might lose more than one million jobs and $1.8 billion annually, as well as $300 million worth of electricity," he said.
The official said Ethiopia has agreed to guarantee just 31 billion cubic meters.
El-Sissi is set to meet with Ethiopia's Prime Minister Abiy Ahmed, winner of this year's Nobel Peace Prize, on Wednesday in the Russian city of Sochi, on the sidelines of a Russia-Africa summit. They may be able to revive talks, but the stakes get higher as the dam nears completion.
Ahmed told Ethiopian lawmakers Tuesday that negotiations are the best chance for resolving the Nile deadlock and that going to war is "not in the best interest of all of us."
"Some say things about use of force," he said, referring to Egypt. "It should be underlined that no force could stop Ethiopia from building a dam. If there is a need to go to war, we could get millions readied. If some could fire a missile, others could use bombs."
Late on Tuesday, Egypt said in a statement it was "shocked" and "surprised" by Ahmed's remarks, which came just days after he was awarded the peace prize.
The statement said it was inappropriate to talk about military options in dealing with the dispute and that it thought the peace prize would have prompted Ethiopia to demonstrate political will, flexibility and "good will toward a binding and comprehensive legal agreement that takes into account the interests of the three countries."
Ethiopia hopes to finish the much-delayed project by 2023. The dam's manager, Kifle Horro, said the project is now 68.5% complete and preparations are underway to finalize power generation from two turbines by next year.
The International Crisis Group, a Brussels-based think tank, warned earlier this year that the "risk of future clashes could be severe if the parties do not also reach agreement on a longer-term basin-wide river management framework."
In recent weeks there have been calls by some commentators in Egypt's pro-government media to resort to force.
Abdallah el-Senawy, a prominent columnist for the daily newspaper el-Shorouk, said the only alternatives were internationalizing the dispute or taking military action.
"Egypt is not a small county," he wrote in a Sunday column. "If all diplomatic and legal options fail, a military intervention might be obligatory."
Anwar el-Hawary, the former editor of the Al-Masry Al-Youm newspaper, compared the dispute to the 1973 war with Israel, in which Egypt launched a surprise attack into the Sinai Peninsula.
"If we fought to liberate Sinai, it is logical to fight to liberate the water," he wrote on Facebook. "The danger is the same in the two cases. War is the last response."
Associated Press writer Elias Meseret in Addis Ababa, Ethiopia, contributed to this report.