South Sudan has laid out conditions for withdrawing its forces from a town in the north it occupied earlier this week.
The office of President Salva Kiir says the south will pull back from Heglig if a "clear mechanism and guarantee" are provided so Sudan can not use the area to attack the south.
It says neutral forces could be deployed until Sudan and South Sudan reach a settlement on the oil-producing area.
Southern forces took control of Heglig on Tuesday, prompting accusations of aggression from the north.
South Sudan's defense minister said Friday that both countries are sending more troops to the frontline after a week of clashes and escalating tension.
The U.N. Security Council has called for a halt to the clashes, which have raised concerns the two Sudans could slip into a full-scale war.
On Wednesday, Sudan announced it was pulling out of talks with South Sudan because of the takeover of Heglig. The south is rejecting calls from the African Union and United Nations to leave the town.
The south says Sudanese warplanes dropped several bombs Thursday near the southern city of Bentiu, killing a soldier.
The African Union has tried to mediate disputes between the two Sudans stemming from the south's independence last year. But the talks in Ethiopia have made little progress.
Key issues include borders, the sharing of oil revenue, and the status of nationals in each other's territory.
Both countries have suggested renewed conflict is possible. Before their separation, north and south Sudan fought a 21-year civil war that ended with a 2005 peace agreement.