Performing http web request to a server requiring SAML authentication - saml

Question

I have simple app that is trying to do a http web request to a server that requires SAML authentication. Authenticated users will get a http response header with a special token, which is what I need to ultimately get.
My app is .net based and does a pretty simple http web request. It does the request then parses the response header. I later traverse the header for the specific token I need:
...
try
{
WindowsIdentity identity = HttpContext.User.Identity as WindowsIdentity;
HttpWebRequest req = (HttpWebRequest)WebRequest.Create(url);
req.UseDefaultCredentials = true;
req.AllowAutoRedirect = true;
req.Timeout = 30000;
HttpWebResponse response = (HttpWebResponse)req.GetResponse();
if (response == null)
{
throw new Exception("No HTTP Response");
}
StringBuilder sb = new StringBuilder();
Byte[] buffer = new byte[8192];
Stream rStream = response.GetResponseStream();
int count = 1;
do
{
count = rStream.Read(buffer, 0, buffer.Length);
if (count != 0)
{
sb.Append(Encoding.UTF8.GetString(buffer, 0, count));
}
} while (count > 0);
...
The problem is that the server I'm requesting requires SAML authentication. It redirects to an ADFS server upon request. My app server currently uses kerberos authentication but I can enable it to do SAML as well. Both servers use the same IdP (ADFS) and are in the same enterprise.
My question is - since my app can also do SAML on the same IdP, is there anyway I could get the necessary claims to connect directly into the destination server?