South Sudan has accused Sudanese troops of crossing into its territory, as tension between the two states rises.
The troops moved about 10km (six miles) into Upper Nile state, Information Minister Barnaba Marial Benjamin said.
On Saturday, Sudan said it would block oil exports from the South after accusing it of backing rebels fighting President Omar al-Bashir’s government.
But Sudanese officials now say the ban will take effect in 60 days. Oil is vital to the economies of both states.
South Sudan became independent in 2011 after decades of conflict with Khartoum and the two neighbours still disagree on several issues.
South Sudan, which gets 98% of its revenues from oil, has massive deposits but is landlocked and reliant on Sudan’s ports for export.
The two countries have long disputed how much the South should pay to use Sudan’s pipelines.
Mr Benjamin said South Sudan would protest to the African Union (AU) and the United Nations about Sudan’s actions.
“They always violate agreements…. Sudan must be brought to book,” he told the BBC’s Newsday programme.
On Sunday, Sudan’s intelligence chief Mohammed Atta said South Sudan had failed to stop supporting rebels operating in Darfur and two border states.
“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,” he said at a press conference in Khartoum, Reuters news agency reports.
Sudan’s Information Minister Ahmed Belal Osman said Sudan planned to close the oil pipelines within 60 days.
However, it would reverse its decision if South Sudan stopped backing the rebels, he said, Reuters reports.
Correspondents say his comments suggest that Sudan is rowing back from a report by state media on Saturday that Mr Bashir had given an order to shut the pipeline.
The Sudanese army is fighting a rebel insurgency in at least three regions.
An umbrella rebel group called the Sudan Revolutionary Front (SRF) has launched attacks on several towns, briefly occupying the major city of Um Rawaba in central Sudan in April.
Sudan and the South came to the brink of war last year, prompting Juba to shut down production – badly hitting both countries.
It only resumed pumping oil in April.