Ethiopia's prime minister Abiy Ahmed said Tuesday his country, Egypt and Sudan have reached a "major common understanding which paves the way for a breakthrough agreement" on a massive dam project that has led to sharp regional tensions and led some to fear military conflict.

"The extraordinary meeting... concluded with all parties reaching a major common understanding which paves the way for a breakthrough agreement," Ahmed's office said in a statement which was posted on Twitter.

South Africa's President Cyril Ramaphosa, a mediator who chaired Tuesday's online meeting of African Union, confirmed there would be further negotiations. 

The statement by Abiy Ahmed's office came as new satellite images show the water level in the reservoir behind the nearly completed 4.6 billion U.S. dollars Grand Ethiopian Renaissance Dam is at its highest in at least four years.  

Ethiopia explained the rising water is from heavy rains, but it has said that it would begin filling the reservoir of Africa's largest dam this month even without a deal as the rainy season floods the Blue Nile. But the new statement says the three countries' leaders have agreed to pursue "further technical discussions on the filling... and proceed to a comprehensive agreement."

The statement did not give details on Tuesday's discussions or what had been agreed upon. But the talks among the country's leaders showed the critical importance placed on finding a way to resolve tensions over the storied Nile River, a lifeline for all involved.

Ethiopia says the colossal dam offers a critical opportunity to pull millions of its nearly 110 million citizens out of poverty and become a major power exporter. Downstream Egypt, which depends on the Nile to supply its farmers and booming population of 100 million with fresh water, asserts that the dam poses an existential threat.

Negotiators have said key questions remain about how much water Ethiopia will release downstream if a multi-year drought occurs and how the countries will resolve any future disputes. Ethiopia rejects binding arbitration at the final stage.

Egyptian President Abdel Fattah el-Sissi stressed Egypt's "sincere will to continue to achieve progress over the disputed issues," a spokesman's statement said. It said the leaders agreed to "give priority to developing a binding legal commitment regarding the basis for filling and operating the dam."

Sudanese Irrigation Minister Yasser Abbas told reporters in the capital, Khartoum, that once the agreement has been solidified, Ethiopia will retain the right to amend some figures relating to the dam's operation during drought periods. "Generally, the atmosphere was positive" during the talks, he said.

Abbas said the leaders agreed on Ethiopia's right to build additional reservoirs and other projects as long as it notifies the downstream countries, in line with international law.

"There are other sticking points, but if we agree on this basic principle, the other points will automatically be solved," he said.

Both Sudanese Prime Minister Abdalla Hamdok and Ethiopia's leader called Tuesday's meeting "fruitful".

"It is absolutely necessary that Egypt, Sudan and Ethiopia, with the support of the African Union, come to an agreement that preserves the interest of all parties," Moussa Faki Mahamat, chairman of the AU commission, said on Twitter, adding that the Nile "should remain a source of peace."

Years of talks with a variety of mediators, including the Trump administration, have failed to produce a solution.

Kevin Wheeler, a researcher at the Environmental Change Institute, University of Oxford, told the AP last week that fears of any immediate water shortage "are not justified at this stage at all and the escalating rhetoric is more due to changing power dynamics in the region.

However, "if there were a drought over the next several years, that certainly could become a risk," he said.

(With input from AP)