How are you trying to access those variables after?

Are you using:

$the_var = Request::get('access_code');

I'm redirecting it to external url and have no idea how they are trying to access them. If I post it through view using <form>, I'm getting desired result from the external url, but not when I'm posting through controller using Redirect.

Ah if you are redirected to an external then you need to either build a query string and submit the vars VIA query string or you need to use CURL and do an actual post from the server.

Using the query string is a little easier to program.

I think this will work

return Redirect::to($url, array('encRequest'=>$encrypted_data, 'access_code'=>$access_code)) 

basically you want to have http://example.com/?encRequest=blah&access_code=somecode

->with message won't work because it creates an environment variable only available in laravel. When you hit an external server the only way to pass variables is query string or within POST data.

If I try your solution, laravel is throwing the below error.

The HTTP status code "1" is not valid

Does that come from your server or the remote one?