With asymmetric cryptography, the sender is not able to encrypt it such that the receiver could have encrypted it without disclosing a private secret without performing a symmetric key exchange. You would have to Once you exchange a symmetric key however, you could symmetrically encrypt the contents of the message and the MAC and then encrypt the shared key with the public key of the recipient. It is then impossible to prove that the message was signed by the sender since either party could have encrypted the message and MAC. I'm not sure if this can be done by the specific library implementation you mentioned though.
That said, I'm not sure why you changed from asking if PGP could do it to asking if asymmetric cryptography could. PGP makes use of both forms of cryptography.