Khartoum has announced it will release tankers carrying oil from South Sudan in a bid to end the standoff over crude exports. The dispute has led to a shutdown of oil production in South Sudan.
Sudan's seizure of the ships escalated a row over transit fees for South Sudanese crude. Efforts to broker an agreement have so far failed.
Omar Al Bashir, Sudan's president, and Salva Kiir, his South Sudanese counterpart, met on Friday on the sidelines of a meeting of East African officials in Ethiopia's capital Addis Ababa to negotiate an end to the dispute.
"President Bashir is ready to make this gesture. Sudan is going to release the vessels detained in Port Sudan," Sayed El Khatib, the deputy head of Sudan's negotiating team, said on Saturday.
However, Pagan Amum, South Sudan's leading negotiator, said on Friday that the meeting between the two presidents had not led to an agreement, and that the shutdown of production would be complete the following day.
Juba has baulked at paying the transit fees demanded by Khartoum. South Sudan this month accused its northern neighbour of "looting" oil worth US$815 million (Dh2.9 billion), and began halting production in protest.
Sudan ratcheted up the tension by retaining tankers filled with South Sudanese oil, claiming it as compensation for unpaid fees. Three ships carrying 2.2 million barrels of oil have been detained, according to the AFP news agency.
Khartoum is demanding $6 for each barrel transported through the Greater Nile Oil Pipeline, while Juba is willing to pay only $1, and is also demanding a $2.4bn financial aid package, as well as the withdrawal of its neighbour's troops from the disputed border region of Abyei.
About two thirds of the 490,000 barrels per day (bpd) production capacity fell to South Sudan after it ceded from the north. While holding the majority of reserves, South Sudan's export options are restricted to the Greater Nile pipeline that channels crude to Port Sudan on the Red Sea Coast.
The economies of both countries are heavily dependent on oil revenues. South Sudan derives 98 per cent of its government income from oil exports, funds it desperately needs to rebuild its infrastructure after the civil war that led to cessation in July.
South Sudan is considering alternative export routes for its crude and has signed an initial agreement with Kenya to build a pipeline and is in talks with Ethiopia over a similar project.
Last month, the French oil major Total said it was considering a pipeline connecting its South Sudanese production assets with new fields in Uganda and Kenya. If exports do not resume, Sudan will add to the crude supply squeeze caused by the latest round of sanctions on Iran, the lack of Syrian and Yemeni oil coming to the market, and the Libyan oil sector's unfinished postwar recovery.
"It's not a huge amount of oil, but it's just one more thing. It does begin to add to something significant," said Robin Mills, an energy analyst at Manaar Energy Consulting in Dubai.
The resulting shortfall increased the burden on the spare production capacity held by Gulf countries, and by Saudi Arabia in particular, said Mr Mills.
The kingdom has pledged to balance the market once sanctions take effect on Iran.