Egypt fears that the $4.6 billion hydropower plant will diminish its share of the river's water flows, arguing its historic water rights must be maintained.
Ethiopia is the source of about 85% of the Nile's water, mainly through rainfall in its highlands, with over 90% of Egyptians relying on water from the Nile's flows.
In June, a panel of international experts tasked with studying the impacts of the Ethiopian dam on lower riparian countries, including Sudan and Egypt, found that the dam project will not cause significant harm to either country.
Cairo remains unconvinced and has sought further studies and consultation with Khartoum and Addis Ababa.
Sudan angered its Egyptian neighbour to the north by accepting the final findings and offering to send experts and technicians to help in the dam's construction, a move welcomed by Ethiopia.
The Sudanese foreign minister is expected to travel to Cairo in the coming days, local media have reported.