Iraq Yehia Rasool, spokesman for the Iraqi commander-in-chief, tweeted that a federal police chief, an intelligence chief and senior officials at the Interior Ministry are among those fired.
Mr Rasool said the deputy minister of interior for intelligence affairs, Lt Gen Amer Saddam, had been dismissed from his post, while Lt Gen Ahmed Abu Ragheef was appointed undersecretary to replace him.
Abdul Karim Abd Fadel, also known as Abu Ali Al Basri, was dismissed from his position as director general of intelligence and combating terrorism at the Ministry of Interior.
He will be replaced by Hamid Al Shatri, deputy head of the National Security Service.
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Back-to-back suicide attacks on a market in central Baghdad killed 32 people and injured 110 on Thursday.
The two bombers detonated their explosives at a secondhand clothes market in the
Bab Al Sharji area, said Interior Ministry spokesman Brig Gen Khalid Al Muhana. He said many poor people use the outdoor market.
The first bomber claimed to be ill but when people gathered around him, he blew himself up, Brig Gen Al Muhana said. The second bomber set off his explosives when people rushed to the scene.
Health Minister Hassan Al Tamimi confirmed the death toll.
ISIS claimed responsibility for the attack in a message posted on the Telegram channel of its Amaq news agency early on Friday.