PGP, GPG and other non-symmetric encryption schemes require two different keys to use them. Each pair of keys can either be treated as two private keys or one public key and one private key. (The two public key case is trivial as it does not offer any proper security.)
One key is used to encrypt the message, and the matching second key is used to decrypt the message. Since the operation of each key is a one way process, it is not possible to decrypt a message even if you have only the key that was used to perform the encryption.
Public encryption and private decryption keys are used to send data securely from multiple sources to a single recipient. This guarantees that only the one recipient can use the data.
Private encryption and public decryption keys allow recipients to guarantee that the data has come from the specific sender.
You can double encrypt messages. A message is encrypted with public key 1 then the results are encrypted again using private key 2. The recipient decrypts with public key 2 and 'knows' that the message originated from the specific source. Anyone can get to this stage using public key 2. However, the message still needs to be decrypted with private key 1 to read the actual contents. Since a private key is involved at both ends, then the transfer is secure.
For your message, you will need the private key that corresponds to the public key used to encrypt the message. As encryption and decryption are both one way processes, you cannot decrypt the message with the key that was used to encrypt it.
If you do not have the private key, then you should contact the sender to find out how you can get the appropriate decryption key.
I hope this helps.