The long-running dispute over Ethiopia's mega-dam is still going nowhere.

But Sudan's prime minister has invited his Egyptian and Ethiopian counterparts for a closed meeting discussion.

It comes after talks hosted by the African Union on Tuesday between Cairo and Adis Ababa failed to reach a binding agreement over the Grand Ethiopian Renaissance Dam (GERD) and the filling of its vast reservoir.

Ever since construction began in 2011, Egypt has regarded the dam as an existential threat to its water supplies, while Sudan fears its own dams would be harmed if Ethiopia fills the reservoir without a deal.

"The case of the water issue cannot be solved through this. It will not be solved through war. At war, you don't know the setting and the final destination. It is harmful," said Ethiopian foreign ministry spokesman Dina Mufti.

"We have to solve this in a modern way, through discussion, and a diplomatic manner, and this is a very thoughtful and useful way of thinking."

The statement said the planned summit will be held by videoconference.

"Prime Minister Abdalla Hamdok invited his Egyptian counterpart Mostafa Madbouli and Ethiopian counterpart Abiy Ahmed to a summit within 10 days to evaluate the negotiations regarding GERD," the premier's office said in a statement late Tuesday.

It said Hamdok expressed concern the dam's construction had reached an advanced stage, making "reaching a deal before the start of operation an urgent and pressing matter".

Last week, Ethiopia offered to share data with Egypt and Sudan, but the proposal was rejected by Khartoum and Cairo which complained of "fallacies" in the figures and an "unacceptable tendency" by Addis Ababa to take unilateral steps.