Egypt's Prime minister arrives in South Sudan from Khartoum. This is the first official visit abroad since the uprising ousted Hosni Mubarak.
Egypt will recognise South Sudan as an independent state after it voted to secede from Khartoum, Egyptian Foreign Minister Nabil Elaraby said.
The new government also said it would introduce a new proposal to Nile Basin nations to try to overcome a stalemate on sharing the river's waters, as a seven-minister delegation headed by Egypt's prime minister arrived on Sunday in Khartoum.
"Sudan intends to be the first to recognise Juba (capital of South Sudan) and Egypt intends to be the second to recognise the South," Elaraby said in Khartoum. The delegation will visit Juba on Monday.
Egypt had pressed for its ally, Sudan, to remain united to preserve 1929 and 1955 Nile Basin treaties, which allocated the lion's share of river waters to Egypt and its southern neighbour, Sudan. But after decades of north-south civil war, southern Sudanese this year voted to become independent on 9 July.
South Sudan has not declared a position on sharing Nile waters but most analysts believe it is likely to side with its east African allies. They have signed a new treaty aimed at ensuring what they say would be a more equitable distribution of the water, worrying Egypt which is struggling to grow food for its burgeoning population.
"We will be offering a new proposal to the Nile Basin states ... and we hope to find a solution which will not harm any nation," Egypt's Water Resources and Irrigation Minister Hussein Ehsan el-Atfi told reporters in Khartoum.
He did not go into details, but Egyptian government spokesman, Magdy Rady, said an unfinished and long-stalled project to create the Jonglei Canal in South Sudan, which would channel swamp water back into the Nile, would be discussed in Juba.
"This is still a project -- we spent a lot of money on it and there's still a little money left to finish it," he said, "This project -- if we finish it -- it will provide 4 billion extra [litres of water a year]."
"This will be divided between Egypt and South Sudan -- if they are not in urgent need of it, we are in urgent need of it."
The two neighbours also agreed a memorandum to connect their national grids, officials from Sudan and Egypt told Reuters.
"Egypt is trying to play a pivotal role in energy to be a hub for the region ... now we are going to Africa through Sudan," said Rady.
War-ravaged Sudan gave Egypt 5,000 cows as a gift to the new government.