"At 8:45 pm (1745 GMT) a number of state security officers came to the home of imam Sadiq Al-Mahdi with a warrant, and they arrested him," his secretary, Mohammed Zaki, told AFP.
Zaki had no further details about the arrest, which makes Mahdi one of the highest-profile figures to be detained in Sudan in recent years.
The National Intelligence and Security Service (NISS) has the right to detain people for more than four months without judicial review.
NISS, which has authority over the RSF, filed a criminal complaint accusing Mahdi of distorting the image of the forces, threatening public peace, undermining the prestige of the state and inciting the international community against Sudan, newspapers reported.
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At a news conference in Khartoum on Wednesday, commanders of the RSF denied their force had looted, raped or committed arson.
"All the allegations against us are lies," an angry Mohammed Hamdan Dalgo, the unit's field commander, shouted.
A senior opposition politician has told AFP that Umma is a main focus of the dialogue process that might lead to a new, coalition government.
The politician said Bashir is pushing for "a real change" because he realises the country is "collapsing".
The security service is resisting the dialogue process, the politician said.
A political scientist, El Shafie Mohammed El Makki, has said that even if Bashir himself is serious about reform, "not all the people in his party are for what is going on. You have to understand this."
Inflation has soared and the Sudanese currency sank. Wars and unrest spread to about half of the country's 18 states, and internal divisions surfaced in Bashir's National Congress Party.