"We will stop all nine agreements, not only oil," Information Minister Ahmed Bilal Osman said at a news conference.
"We are still committed to have good relations with South Sudan and if they are serious about implementing the nine agreements we can return to cooperate with them."
His comments followed an order yesterday from President Omar al-Bashir to shut the pipeline carrying South Sudanese crude for export.
Bashir's command came after he warned the South over backing rebels, who analysts say humiliated the authorities with recent attacks.
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Osman, along with Sudan's intelligence chief Mohammed Atta, confirmed that the oil shutdown had begun.
Despite that, Osman said that some South Sudanese oil had already reached the Port Sudan export terminal and the South is free to sell it -- as long as it pays the fees owed to Khartoum.
After months of intermittent clashes, Sudan and South Sudan agreed in early March to detailed timetables for normalising relations by setting up a border buffer zone and implementing eight other key pacts.
South Sudan separated two years ago with most of the formerly united Sudan's oil production but the export infrastructure remained under northern control.
Last September the two nations agreed to the nine pacts but they did not take effect as Khartoum pushed for guarantees that South Sudan would no longer back the rebels.
In March, Juba and Khartoum finally agreed on detailed timetables to set all the deals in motion. A month later Bashir visited Juba, symbolising the then-easing of tensions.
"We will continue to implement the terms of the co-operation agreement," South Sudanese Information Minister Barnaba Marial Benjamin told reporters.