The two leaders agreed to "encourage the formulation of joint development projects to ensure the optimal exploitation of hydraulic resources within the framework of the Nile Basin Initiative, notably involving countries east of the river: Egypt, Ethiopia and Sudan," Amare Girma said after the talks in in the Egyptian Red Sea resort.
Colonial-era agreements imposed by Britain prohibited Nile basin states other than Egypt from undertaking projects that would reduce the river's flow.
But in 1999 Egypt finally agreed with the other nine littoral states to thrash out a new framework for sharing the river's resources.
More than 95 percent of Egypt's water needs are covered by the Nile but according to official estimates the country, whose population has increased at least three-fold since 1959 bringing it up to 72 million, now registers a deficit and needs to develop new hydraulic resources.
Some 85 percent of the Nile's flow comes down the Blue Nile from Ethiopia.
Egypt's independent press regularly writes about dam construction projects underway in Ethiopia, allegedly in cooperation with Israel, which could slacken the flow of water and affect Cairo's Nile water supply.
A meeting gathering all 10 Nile basin states is scheduled for May in Uganda, Amare said.
Mubarak and Meles also examined the agenda of a New Partnership for Africas Development (NEPAD) summit in Sharm el-Sheikh next Tuesday, the Egyptian president's office said.
NEPAD aims to bring Africa out of under-development by attracting private investment, in return for a commitment by the African states to good governance.
Some 30 heads of state and governments are expected to attend.
Meles arrived in Cairo on Saturday for a visit during which he will attend the NEPAD meeting.