The African neighbours, which split apart in July, have clashed repeatedly along their 1,800 km (1,200 miles) long border, parts of which passes close to oilfields.
The two edged close to resuming full-blown war in April when South Sudan's army seized the Heglig oil region, before withdrawing in the face of international pressure, Reuters reports.
The African Union (AU) has managed to bring back both sides to the negotiation table but talks broke off last week over disputes over the positing of their boundary line.
South Sudan's chief negotiator Pagan Amum said international arbitration was the best way to determine the status of the disputed border areas.
"Let the government of Sudan join us to go to arbitration because arbitration is the most civilised way and most peaceful way to resolve this dispute over the border. You don't need to fight for this border," Amum told reporters in the South Sudan capital Juba.
"South Sudan will go with its maps and documents and records showing that these are territories within South Sudan," he said, gesturing at a map dated May 2, 1955, which showed Heglig and portions of other disputed areas falling on his side of the border.
Amum said AU talks in Addis Ababa would continue on June 19 but there was no immediate confirmation from Sudan.
Sudan said it did not rule out international arbitration but added such as request raised the question whether Juba was serious about the talks.
"The request from the government of South Sudan ... raises doubts whether it is serious about continuing the talks," the Sudanese foreign ministry said in a statement, adding that Juba's claim on Heglig was a "hostile" act.
Both sides have produced their own set of border maps to support land claims during the talks.
South Sudan became independent in July under a 2005 peace agreement that ended decades of civil war with Khartoum but both sides are at loggerheads over a list of disputes.
Apart from marking their border both sides also need to agree on how much the landlocked South should pay to export crude oil through Sudan.
Juba shut down its entire output of about 350,000 barrels per day in January to stop Khartoum seizing oil as compensation for what it called unpaid fees.
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