UN rights chief Navi Pillay on Thursday called for an \"immediate investigation\" into the circumstances surrounding the February death of an unarmed black US teen, shot by a neighborhood watchman. Pillay made the comments about the controversial Trayvon Martin case at a press conference in Barbados, as she wrapped up a three-day visit to the Caribbean island nation. \"As High Commissioner for Human Rights, I call for an immediate investigation,\" Pillay told reporters. \"Justice must be done for the victim. It\'s not just this individual case. It calls into question the delivery of justice in all situations like this.\" Neighborhood watch captain George Zimmerman, a white Hispanic, fatally shot 17-year-old Martin inside a gated community in the Florida town of Sanford on February 26. Zimmerman has said he acted in self-defense after Martin punched him in the nose, knocked him down and slammed his head into the ground. The case has unleashed a national uproar over race relations and the right to self-defense in the United States. Pillay expressed shock that Zimmerman was not arrested right away, and expressed concern about Florida\'s \"Stand Your Ground\" law, which allows the use of deadly force in situations where there is a belief of a threat. \"The law should operate equally in respect of all violations. I will be awaiting an investigation and prosecution and trial and of course reparations for the victims concerned,\" Pillay said. Sanford police applied for a warrant to arrest Zimmerman in the early stages of the investigation, local media including The Miami Herald reported. Prosecutors however held off approving the warrant, pending further review. Since Martin\'s death, there have been numerous large public protests calling for Zimmerman\'s arrest, but there have been no detention orders and the 28-year-old has gone into hiding, fearing for his life.