A South Sudan diplomat said negotiators for the two countries began meeting Thursday and that Sudanese President Omar al-Bashir met with South Sudanese President Salva Kiir, the Voice of America reported.
Former South Africa President Thabo Mbeki was mediating the summit.
"It's just the commitment for the implementation of what has been agreed, there is no new issue to be agreed," said Arop Deng, South Sudan's ambassador to Ethiopia.
Oil -- a key source of revenue for both countries -- that is produced in South Sudan will not resume flowing through Sudan's pipelines until the agreements are implemented, he said.
Oil revenues are a fundamental source of income for both countries.
Security is also a sensitive issue between the two countries. Sudan and South Sudan nearly broke into war in April over disputes about the Abyei region, which both countries claim.
Under the agreements, Sudan and South Sudan will establish a border demilitarized zone, with each country withdrawing its troops for at least 6 miles.
Ethiopian Prime Minister Hailemariam Desalegn has tried to persuade the two presidents to resolve their issues quickly.
"We don't need a war or conflict between the two because that has an impact on us. As much as regional stability has an impact on us for our development, for our prosperity, for our democratization process, the regional instability in our neighboring countries will affect us," Ethiopian Foreign Ministry spokesman Dina Mufii said. "So in that sense, we think whatever negative things that happen in Sudan would negatively impact us."
South Sudan gained independence in 2011 from Sudan after a peace agreement that ended decades of war.