It is not possible to click using PHP because form submission is the action on the client's side, i.e in your browser. Events in the browser like this can be executed by javascript or other client language.
<form ... >
<input type="submit" name="rregjistro" value="Rregjistro" />
<!-- remove onclick attribute for now -->
</form>
<div id="myResult"></div>
<script>
$(function(){
$("input[name=rregjistro]").click(function(){
// url needs to belong to your domain
$.ajax({url: "/your_url_path", success: function(result){
$("#myResult").html(result);
open();
}});
});
});
</script>