South Sudan warned its neighbour Sudan that turning off oil flows through pipelines between the two countries could destroy the link unless production resumed within a few months.
South Sudan last week started shutting down oil production after Sudan said it would close the pipelines within 60 days unless South Sudan ended support for Sudanese rebels. Juba denies backing them.
Landlocked South Sudan exports oil through Sudan's Red Sea terminal in the absence of its own export facilities.
Oil Minister Stephen Dhieu Dau said South Sudan had urged Sudan to reverse its threat to close the pipelines.
Sudan's Oil Minister Awad al-Jaz said it was up to South Sudan to cut ties with insurgents operating across the shared border if it wanted oil flows to continue, state news agency SUNA said. "The ball is still in South Sudan's court," he said.
The African Union is trying to mediate in the row between the neighbours which came close to war in April 2012, the worst violence since the South seceded in 2011.
Dau said pipelines would have to be flushed with water to avoid galling, which was accelerating the rusting of the metal.
He said if oil did not flow within several months, the pipeline would be a "total loss for the investors and the owners. It is not much our concern."
The pipelines and other facilities in both countries were mainly built by China before formerly-united Sudan split in a messy divorce in 2011. China National Petroleum Corp, Malaysia's Petronas and India's ONGC Videsh run the oilfields in South Sudan together with the government.
South Sudan only restarted oil production in April after ending pumping around 300,000 barrels per day in January 2012 when the former civil war foes failed to agree on pipeline fees.
Dau said engineers had so far started closing wells in the Palouge field in blocks 3 and 7 while the shutdown of other smaller blocks in Unity state would start July 25.
He gave no new production figures, saying only it was less than 180,000 barrels a day last measured on Friday.
South Sudan relies on oil and foreign grants for most of its budget.
The shutdown is also likely to hit Sudan, which has been struggling with turmoil since losing most oil reserves with South Sudan's secession. Oil fees from Juba are essential to bring down soaring inflation, which stokes dissent.