"We plan to close the oil pipelines within 60 days ... but we might reverse the decision," Ahmed Belal Osman told reporters, without elaborating. "The door is open for rational thinking ... but we won't allow the support of rebels."
Sudan's President Omar Hassan al-Bashir said on Saturday it would halt the south's oil exports through northern facilities because of its alleged backing of rebels operating on Sudanese soil. South Sudan denies it offers any such support.
The order to shut pipelines from landlocked South Sudan through Sudan to a port on the Red Sea - the south's only route to market - came only three months after the countries ended a bitter dispute over crude.
Sudan and South Sudan, which split into two countries in 2011 after decades of war fuelled by oil and ethnicity, agreed in March to restart the crude flow after a 16-month shutdown triggered by an argument over transit fees and territory.
Sudan's top intelligence chief Mohammed Atta said Khartoum had repeatedly provided South Sudan's President Salva Kiir with proof of his country's support for rebels operating in the western region of Darfur and two border states.
"We asked him to stop this support," Atta said in a rare public appearance. "They (rebels) get supplied with weapons, ammunition, petrol, spare parts for cars, food ... They send their wounded to hospitals in the south. Tens of wounded (rebels) are now being treated in the south."
South Sudan's crude had only just started to move through the two pipelines in May, with the first cargoes sold last week for shipment from Port Sudan.
It can be very costly to close the pipelines, which can become blocked if the waxy oil stops halfway. South Sudan would also have to shut down its entire oil production because it has no storage facilities.
A confirmed oil stoppage would dash hopes of an economic lifeline to both of the underdeveloped countries. The last shutdown ravaged their economies because oil was the main source of revenue to pay for food imports.