JOHANNESBURG: Ethiopia's prime minister 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 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 Grand Ethiopian Renaissance Dam is at its highest in at least four years.

Ethiopia has said the rising water is from heavy rains, and the new statement said that "it has become evident over the past two weeks in the rainy season that the (dam's) first-year filling is achieved and the dam under construction is already overtopping."

Ethiopia has said it would begin filling the reservoir of the dam, Africa's largest, 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, mediated by current African Union chair and South African President Cyril Ramaphosa, 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.

Now satellite images of the reservoir filling are adding fresh urgency. The latest imagery taken Tuesday "certainly shows the highest water levels behind the dam in at least the past four years," said Stephen Wood, senior director with Maxar News Bureau.

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.