export public key from keychain access
When you export you private key, you should get a .p12 file. Import that file on the other machine. It should have everything in it you need. You don't need to specifically export and import the public key.
It's been broken since 2009 as reflected in this bug report.
In case that report wanders off the internet, here's the relevant instructions to import a public key pem file. You'll want to execute this in Terminal.
security import pub_key.pem -k ~/Library/Keychains/login.keychain