Landlocked South Sudan began halting oil production last week after accusing Sudan of stealing $815 million worth of the south's oil. Sudan detained the oil tankers loading oil from the south in Port Sudan in response.
But Sudanese President Omar al-Bashir decided Saturday to "release the vessels detained in Port Sudan as soon as possible," said Sayed al-Khatib, a spokesman for Sudan's negotiation team.
Al-Khatib also said al-Bashir is ready to sign an agreement with South Sudan's president Salva Kiir "by the end of today".
Al-Khatib said all parties were ready to sign a deal alongside a meeting of East African leaders on Friday in Ethiopia's capital Addis Ababa.
"This would have meant that we could leave the crisis behind us," he said.
But a South Sudan official said Friday that talks between Kiir and al-Bashir to end an oil dispute had failed because of Sudan's "continued stealing of oil".
Pagan Amum, secretary general of South Sudan's ruling party, said South Sudan would now "turn east" to export its oil to Kenya and Ethiopia.
South Sudan has already signed a memorandum of understanding with Kenya to build a pipeline from its oil fields to Kenya's northern coast, where a new port is planned.
South Sudan, which broke away from its northern neighbour Sudan on July 9 last year, said it had also approached Ethiopia about developing a new pipeline that would go through Ethiopia to a port in the tiny nation of Djibouti.
Amum said the two would only end their dispute if Sudan "reimburses the full amount of stolen goods".
Sudan claims it is entitled to the South Sudanese oil it has taken because it has not received any transit fee payment after the two countries split.
"If it is proven that we have taken one barrel more than the equivalent in kind that is something we have to be held responsible for," al-Khatib said.
The oil negotiations between the two neighbours have been in a deadlock for two years. They have never agreed on the transit fees South Sudan should pay to Sudan for using its infrastructure of port and pipelines.
A shutdown means both countries risk losing hundreds of millions of dollars. Sudan also risks losing future revenue if South Sudan builds new pipelines that do not cross its territory.