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Zoran Vlajic is being investigated by South African police for illegal gun possession and fraud.
The department told the paper it did not know the Serbian government had not renewed Vlajic's passport.
An e-mail sent by former Serbian consul Jasmina Stankovic Tatarac confirmed Vlajic's passport had never been renewed, the weekly reported. Serbian passports cannot be renewed or extended; instead a new passport must be issued.
Home affairs spokeswoman Manusha Pillai said the department was investigating the case.
"The department discovered that Mr Zoran Vlajic misrepresented himself by submitting a fraudulent copy indicating an extension of his Serbian passport in his application for permanent residence," she was quoted as saying.
