How to prevent browser from prompting for a client certificate and allow the IIS to accept it (not requres it)?

In a web application, I have a WCF service uses Client Certificate authentication. I checked "Accept Client Certificate" in IIS - SSL Settings and it works fine. But some times, in some browsers, if a certificate is installed on the client machine, the browser is prompting a message to choose the certificate it wants to provide to the server which is not a desirable behavior since only the web service needs the certificate.

How can I handle it without creating an independent web project for the web service on IIS?