Bashir this week said he would stop oil deliveries from South Sudan in response to fighting along the border. Sudan confirmed last week that it was getting oil from South Sudan after officials agreed in April to resume bilateral cooperation.
South Sudanese government spokesman Barnaba Marial Benjamin said oil was flowing over the border.
"Now the oil is still flowing smoothly, it's on its way to Port Sudan, that I can assure you," he was quoted by Voice of America as saying. "Of course President Bashir sends a threat that if we continue to supply the rebels, as he claims, that he has got two weeks to go or he will close down the oil."
South Sudan gained independence from Sudan in 2011 under the terms of a peace deal brokered with help from the U.S. government. South Sudan gained control over oil fields, though Sudan maintains authority over export infrastructure.
Conflicts last year in the oil-rich area of Heglig, near the shared border, nearly pushed the countries to war.