ADDIS ABABA - The presidents of Sudan and South Sudan met for a second day Monday as pressure mounts to settle long-running bitter disputes that have brought the rivals to the brink of renewed conflict.Former civil war foes President Omar al-Bashir of Sudan and his Southern counterpart Salva Kiir are facing the looming threat of UN Security Council sanctions unless they reach a deal, after they missed a Saturday deadline. The protracted talks under African Union mediation began in the Ethiopian capital several months before South Sudan split in July 2011 from what was Africa's biggest nation, following an independence vote after decades of war.The leaders met Monday for talks hosted by Ethiopian Prime Minister Hailemariam Desalegn in the presidential palace, alongside AU chief mediator and former South African president Thabo Mbeki."The presidents met, now they are discussing issues," including contested border areas and oil, said top South Sudanese official Deng Alor, as the leaders broke mid-morning for discusions with their own teams.Face-to-face meetings expected to resume later Monday, Alor added. The pair kick-started the talks with a two-hour meeting late Sunday, following marathon efforts by rival delegations to close gaps on a raft of issues left unresolved when the South became independent last year.Little information has filtered out about progress of the meeting, but both leaders have been seen smiling and chatting in each other's company."There is still optimism some form of a deal can be settled," said a Western diplomat.Key issues include the ownership of contested regions along their frontier -- especially the flashpoint Abyei region -- and the setting up of a demilitarised border zone after bloody clashes.The buffer zone would also potentially cut support for rebel forces in Sudan's Southern Kordofan and Blue Nile regions that Khartoum accuses Juba of backing. The UN set a deadline for a deal 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 bombing raids in response.UN leader Ban Ki-moon has called on the leaders to tackle their remaining differences, "so that their summit concludes with a success that marks an end to the era of conflict".For once, the mood in the long-running talks appeared largely positive, with both Khartoum and Juba apparently keen to end conflict and a stalemate over stalled oil production that is crippling both their economies.While the two leaders have met several times in recent months, delegates said there was a real sense some form of a deal was possible. A comprehensive deal -- as opposed to another stepping-stone agreement -- would have to include settlement on Abyei, a Lebanon-sized border area claimed by both sides and currently controlled by Ethiopian peacekeepers. But amidst the diplomatic optimism, there seemed little chance of a breakthrough to solve the growing humanitarian crises in Sudan's civil war states of Southern Kordofan and Blue Nile.However, it was hoped the summit would settle the details of last month's deal to fix the oil export fees that landlocked South Sudan will pay to ship crude through Khartoum's pipelines to the Red Sea.At independence, Juba took two-thirds of the region's oil, but processing and export facilities remained in Sudan. In January, the South shut off oil production after accusing Sudan of stealing its oil.