winhttpcertcfg: Granting certificates with for windows service user

I'm stuck with granting client certificates in Windows Server 2003 with winhttpcertcfg :(

My cert is correctly installed in LOCAL_MACHINE\My keystore and I granted it with winhttpcertcfg.exe. So everything looks good to me:

WinHttpCertCfg.exe -l -c LOCAL_MACHINE\MY -s "MY_CERT"

Additional accounts and groups with access to the private key include:

NT AUTHORITY\SYSTEM

BUILTIN\Administrators

But when I try to access MY_CERT in a windows service which is logged on as local system account I get the following Exception:

System.Net.WebException: The request was aborted: Could not create SSL/TLS secure channel.

Log-Details:

System.Net Information: 0 : [0600] AcquireCredentialsHandle(package = Microsoft Unified Security Protocol Provider, intent = Outbound, scc = System.Net.SecureCredential)

System.Net Error: 0 : [0600] AcquireCredentialsHandle() failed with error 0X8009030D. System.Net.Sockets Verbose: 0 : [0600] Socket#21936442::Dispose()

System.Net Error: 0 : [0600] Exception in the HttpWebRequest#24862511:: - The request was aborted: Could not create SSL/TLS secure channel.

System.Net Error: 0 : [0600] Exception in the HttpWebRequest#24862511::EndGetResponse - The request was aborted: Could not create SSL/TLS secure channel.

Everythings works fine if the windows service is logged on as another user. What's the problem with local system account accessing the keystore?

Any suggestions?