script.js

document.onmousemove = function(e){
  var rect = document.getElementById('r');
  rect.setAttribute('x',e.clientX-(rect.getAttribute('width')/2));
  rect.setAttribute('y',e.clientY-(rect.getAttribute('height')/2));
};

document.onclick = function(e){
  var point = document.createElementNS("http://www.w3.org/2000/svg",'rect');
  var rect = document.getElementById('r');

  point.setAttribute('x', e.clientX-50);
  point.setAttribute('y', e.clientY-50);
  point.setAttribute('width', 100);
  point.setAttribute('height', 100);
  document.getElementById('root').appendChild(point);
}

svg-stylesheets.css

svg {
  cursor: none;
}
rect {
  fill:red;
  stroke:black;
  stroke-width:5;
  opacity:0.5
}

test.svg