ADDIS ABABA, Ethiopia (AP) -- The presidents of Sudan and South Sudan agreed Saturday to the unconditional and speedy implementation of deals reached in September to demilitarize their shared borders and allow oil exports to flow from South Sudan's oil fields north through Sudan's pipelines, an African Union official said.

Sudan President Omar al-Bashir and South Sudan President Salva Kiir met on Friday and Saturday in Ethiopia's capital to revive a stalled oil exportation deal that has lagged for months over disputes on the setup of security arrangements in the border regions.

AU mediator Thabo Mbeki told reporters late Saturday that the two presidents agreed to the "speedy, unconditional and coordinated" implementation of the agreements.

"We are very, very pleased indeed with the outcome of this because it has indeed opened the way for the implementation of all of these various agreements," said Mbeki. "They have also agreed that action should be taken immediately, as soon as possible, to implement all the existing agreements unconditionally."

AU mediators will present officials of the two sides the timetable for oil exports and the withdrawal of military forces from border areas. The schedule will be ready by Jan. 13, Mbeki said.

"The presidents agreed that steps should be taken without any further delay to demarcate those parts of the border which have been agreed," said Mbeki.

Ethiopian Prime Minister Hailemariam Desalegn hailed the two leaders' agreements. Hailemariam last week went to both capitals to help move the process forward. The two sides fought a decades-long war and still don't trust each other. South Sudan alleged that Sudan carried out attacks against its territory even when Hailemariam was in the Sudanese capital Khartoum.

The two sides are still at odds over some disputed areas, including the contested Abyei region.

South Sudan chief negotiator Pagan Amum on Friday said that in case of disagreements over the recommendation of the mediators, his country is proposing to go to binding international arbitration.  There was no agreement on the issue during the summit and AU officials say how the two sides would proceed in such events remains open ended.

South Sudan held a vote and broke away from Sudan in 2011. South Sudan was pumping its oil through Sudan's pipelines up until early 2012, when it accused Sudan of stealing its oil. That decision has crippled government budgets in both countries.