Bashir issued a presidential decree announcing Salah Abdallah Mohammed Salih as the new head of the country's National Intelligence and Security Service, SUNA said, without providing further details.
Salih had previously headed NISS and was replaced by Atta in August 2009.
Atta's removal comes at a time when NISS is leading a crackdown on sporadic opposition protests that have erupted from early January against rising food prices.
Protesters have taken to the streets in recent weeks after bread prices jumped following a government decision to leave wheat imports to the private sector that triggered a sharp rise in the cost of flour.
NISS agents have also arrested several senior leaders of opposition groups since January in a bid to prevent the protests from spreading.
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