FIFA said it did not recognise the Sudanese Football Association (SFA) vote on July 26 which elected Mutasim Jaafar as the new president because the government barred the former SFA chief from standing for a third term.
World football's governing body, which requires governments to refrain from meddling in national football federations, said earlier that other candidates had also been barred.
"FIFA's Emergency Committee decided not to recognise the results of the elections and to set a deadline of 15 August 2010 to hold new elections in compliance with the SFA Statutes and without any influence of third parties," FIFA said in a statement sent to Reuters on Tuesday.
A possible suspension, the usual punishment from FIFA for government interference, would threaten Sudan's eligibility to play their opening African Nations Cup qualifier against Congo on September 3.
"We will try to do our best to deal with the matter and avoid any kind of misunderstanding between FIFA, the SFA and the government," he told Reuters.
"The government would have to give permission for any rerun otherwise they too would not recognise the elections," he said, adding Sudan must tread carefully to avoid FIFA sanctions.
