HTTP status 403: Forbidden exception using certificate to authenticate access to ASP.NET web service

I have an ASP.NET web service deployed on //service/webservice and I want my ASP.NET web application (app1) on the //web1 to access the web service with certificate authentication. I keep getting  System.Net.WebException: The request failed with HTTP status 403: Forbidden exception. The follwoing is my setup:

On certificate export;
I exported a server certificate issued to //service from LocalMachine store and saved it as service.cer.
I also exported a client certificate issued to //web1 from LocalMachine store and saved it as web1.cer

Setup on //service/webservice:
- On Directory Security, unchecked Anonymous Access and all Authentication Access (Integrated Windows Access, Digest Authentication and Basic Authentication).
- On Secure communications, checked Required secure channel(SSL), Require 128-bit encyption, Require client certificate, and Enable client ...