Citing security sources, SUNA news agency said al-Fadel and al-Basha were among 14 people, including retired army officers, taken in for questioning about "a plot aimed at damaging national security and creating trouble in the capital."
SUNA said among those arrested was retired general Mohammed Ali Hamed, a former deputy head of the security services.
The semiofficial Sudan Media Centre quoted what it described as a high-ranking security official as saying that the arrests were made after the government discovered plans to "stage an act of sabotage that seeks to undermine the security of the country and instigate havoc in Khartoum and cause chaos".
The report indicated the plotters had secured the assistance of retired officers in the army, especially those from the Blue Nile and Nuba Mountains areas.
The security services had known of a plot since April and decided to act on Saturday "to preserve national security", SUNA said, adding that the 14 had been in contact with foreign countries. It did not elaborate.
Al-Fadel had served as adviser of Omar al-Bashir, the Sudanese president, but left in 2004 and rejoined the opposition Umma party, the largest opposition force in the country.
He later split from the Umma party and found his own opposition political grouping of the Umma Islah wa Tajdid.