Interior Minister Mauricio Lopez said Mr Corado had implemented new disciplinary measures in the jail.
BBC: Guatemala prison director 'killed by prison gang'
Director of El Infiernito prison Amilcar Corado was ambushed by four gunmen on motorcycles.
But Mr Lopez said the prisoners were wrong if they thought the authorities would back down after Mr Corado's murder.
Mr Corado had been in put in charge of the prison 15 days ago and had introduced new disciplinary measures.
Mr Corado had taken over control of the high-security El Infiernito jail after serving as governor in a prison in the capital.
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