No. Unfortunately, you are not able to retrieve deleted messages from your Facebook account.
However, immediately after you delete a message in your Messages Inbox, you are given the option to "Undo" the deletion, but that is the only time you will be able to recover the message. Once a message is deleted, it's gone and there is no way to retrieve it later (apart from a court order).
Keep in mind, that the deleted messages will still be visiable in your friends Messages Inbox when you delete a message from your account (unless they also deleted the messages). So one of your best chances at recovering the messages is to contact the recipient (or sender) of the messages and ask them to send you a copy of the Facebook messages.
Another option... If you get an email when someone sends you a Facebook message, you could also check your email, as that will have a copy of the message that was sent.