Afriforum says the decision to "shift" crime intelligence unit head Richard Mdluli to another position did not resolve problems within the SA Police Service.
AfriForum's Nantes Kelder says moving Mdluli is not the answer - the problem must be dealt with head-on and not moved around.
Earlier, Police Minister Nathi Mthethwa told the National Assembly that Mdluli's new position would be determined by acting national commissioner Nhlanhla Mkhwanazi.
Allegations of mismanagement of funds and nepotism had been levelled against Mdluli.
Kelder called for Mdluli to be suspended, pending investigations, rather than moved to a new position.
The Democratic Alliance also called on President Jacob Zuma to re-suspend Mdluli with immediate effect.
It said anything less is unacceptable.
