Sudanese President Omar al-Bashir.
The rival delegations have held dragging talks that began several months before South Sudan split Africa's biggest nation in two in July 2011, when it seceded after a landslide independence vote following decades of war.
Among issues on the table on Sunday are expected to be ownership of contested regions along their frontier — especially the flashpoint Abyei region — as well as the setting up of a demilitarised border zone after bloody clashes.
The buffer zone would also potentially cut support of rebel forces in Sudan's crisis-hit Southern Kordofan and Blue Nile regions, where Sudan accuses Juba of supplying former civil war comrades Khartoum now seeks to wipe out.
Multiple rounds of talks have failed to find solutions, but both sides have said they are now optimistic, amid the looming threat of United Nations Security Council sanctions, and the positive sign of the presidents meeting face-to-face.
"We are still facing difficulties … but we are hopeful we can reach a deal," said Atif Kiir, spokesperson of South Sudan's delegation to the African Union mediated talks in the Ethiopian capital.
"The summit is to reach a comprehensive agreement between the two countries, so let us hope," his Sudanese counterpart Badr el-din Abdullah told reporters late on Saturday, in a brief break from negotiations that stretched into the night.
Deadline
A UN deadline passed on Saturday for Sudanese President Omar al-Bashir and his Southern counterpart Salva Kiir to settle the raft of key issues unresolved when the South became the world's newest nation last year.
The deadline was set after brutal border clashes broke out in March, when Southern troops and tanks briefly wrested the valuable Heglig oil field from Khartoum's control, and Sudan launched brutal bombing raids in response.
UN leader Ban Ki-moon has called on leaders to "take responsibility for the resolution of their remaining differences, so that their summit concludes with a success that marks an end to the era of conflict".
While Kiir arrived on Saturday, Bashir was expected to land on Sunday morning, first meeting with Ethiopia's Prime Minister Hailemariam Desalegn, before meeting his counterpart for talks later in the afternoon.
In the bustling lobby of an upmarket hotel, a mix of delegates, diplomats, rebel leaders, technical advisors, journalists and wealthy tourists rubbed shoulders, as meetings continued late into Saturday night.
For once, the mood in these long running and often slow moving talks appeared positive, with both Khartoum and Juba apparently keen to end conflict and a mutually economically crippling stalemate over stalled oil production.
Chief mediator Thabo Mbeki, the former South Africa president, was seen busily shuttling between multiple delegations addressing issues of security, border demarcation, oil and finance.
"There does seem a genuine move towards finding a broad solution, even if technical issues and details will certainly need fixing in future meetings," said a Western diplomat close to the talks.
"We are not going to go back to fighting each other, we know the cost of that after 50 years of war," said the South's spokesperson Kiir. "It is the time to rebuild our lives, to rebuild our nation." – AFP