Egypt fears the project will significantly reduce its share of the water from the Nile - the river provides almost all of Egypt's freshwater. Ethiopia, on the other hand, says the GERD will not have any effect on Egypt's share of water and claims the project is necessary for its economic development.
The Egyptian ministry said that Ethiopia's delegation refused to discuss a proposal on filling and operating what will be Africa's largest hydroelectric dam.
The statement urged Ethiopia to engage in "serious technical negotiations" at September 30-October 1 talks in Sudan's capital, Khartoum.
The dam also promises economic benefits for Sudan.
Separately, a note circulated to Egyptian diplomats last week showed the extent of the two countries' differences, Reuters news agency reported.
The note distributed by the Egyptian foreign ministry, a copy of which was seen by Reuters, said Ethiopia has "summarily rejected" its plan for key aspects of operating the dam and dismissed Ethiopia's proposal as "unfair and inequitable".
It pointed to key differences over the annual flow of water that should be guaranteed to Egypt and how to manage flows during droughts.
A spokesperson at Ethiopia's foreign ministry, Nebiat Getachew, said on Monday the meeting had so far produced no agreements or disagreements and gave no immediate response to the Egyptian claims.
GERD was announced in 2011 and is designed to be the centrepiece of Ethiopia's bid to become Africa's biggest power exporter, generating more than 6,000 megawatts of electricity.
In January, Ethiopia's water and energy minister said that, following construction delays, the dam would start production by the end of 2020 and be fully operational by 2022.
Although nationalist, and sometimes belligerent, rhetoric between Egypt and Ethiopia over the issue has cooled in recent years, the sides have remained deadlocked.
Egypt said in the note seen by Reuters that it shared its proposal for filling and operating the dam with Ethiopia and Sudan on July 31 and August 1, inviting the two countries for a meeting of foreign and water ministers.
"Unfortunately, in a letter dated August 12, 2019, Ethiopia summarily rejected Egypt's proposal and declined to attend the six-party meeting," it said.
Addis Ababa had instead proposed a meeting of water ministers to discuss a document that included an Ethiopian proposal from 2018, it said.
Both proposals agree that the first of five phases for filling the dam should take two years, at the end of which the GERD's reservoir in Ethiopia would be filled to 595 metres (1,952 feet) and all the dam's hydropower turbines would become operational.
However, the Egyptian proposal says that if this first phase coincides with an extreme drought on Ethiopia's Blue Nile, similar to that experienced in 1979-1980, the two-year period should be extended to keep the water level at Egypt's High Aswan Dam from dropping below 165 metres (541 feet).
Without such a concession, Egypt says it would risk losing more than one million jobs and $1.8bn in economic output annually, as well as electricity valued at $300m.
After the first stage of filling, Egypt's proposal requires a minimum annual release of 40 billion cubic metres (52 billion cubic yards) of water from the GERD, while Ethiopia suggests 35 billion cubic metres (46 billion cubic yards), according to the Egyptian note.
The note cites Ethiopia as saying last month that Egypt's proposal "put(s) the dam filling in an impossible condition," a charge Egypt dismisses.
"The Ethiopian proposal ... overwhelmingly favours Ethiopia and is extremely prejudicial to the interests of downstream states," it says.