initializing a Map<string,string> in Typescript from json object

I have a class in Typescript containing a map:

public map:Map<string,string>;
constructor() {
  let jsonString = {
    "peureo" : "dsdlsdksd"
  };
  this.map = jsonString;
}

Problem is that the initialization doesn't work.

jsonString is something that I will receive from a Java Object serialized to Json.

Anyone can help? Thanks!