This weekend's attack marks the biggest push by a rebel alliance that is seeking to topple President Omar Hassan al-Bashir
"Bashir ordered the minister of oil to stop the flow of South Sudanese oil from tomorrow, Sunday," Radio Omdurman reported in an SMS message which gave no further details.
The oil, which has not yet reached Sudan's Red Sea export terminal, would be worth billions of dollars in revenue to both impoverished nations if exports resumed.
Bashir had warned on May 27 that he would block the oil if the South's government in Juba provides assistance to rebels fighting in South Kordofan and Blue Nile states, or in the Darfur region.
Bashir threatened to "completely close the pipeline".
Juba denies supporting the rebels. – AFP