Fe pública is defined as la facultad con la que están investidos determinados agentes para certificar que los hechos que les constan son verdaderos y auténticos.* I have seen fe pública translated literally as “public faith” and “public trust, renderings that admittedly don’t reflect the meaning of the expression, and as “affidavit,” a term denoting a sworn statement (declaración jurada) that may be made by any individual and not necessarily by the agents authorized to do so as in the definition above.
The act itself (el hecho de “dar fe”) has sometimes been rendered as “notarial attestation,” a possible translation if the certifying authority (fedatario público) in question is a notary public. Indeed, although most often associated with notaries, fedatario público refers to anyone authorized to ejercer la fe pública (i.e., to issue documents certifying a given event as true and authentic). Thus there is fe pública notarial, fe pública judicial, fe pública registral, fe pública administrativa, etc., and fedatarios públicos include not only notaries, but also court clerks, registrars and certain authorized civil servants. Moreover, if certification is required in a foreign country, the local Spanish consul ejerce la fe pública in his jurisdiction.
*Diccionario del español jurídico de la RAE
Léxico Jurídico Español-Inglés 
Yes, this is a tough one. I agree that “public faith” and the like are unlikely to help readers understand what’s going on. West’s translation/description is helpful: “the legal authority to attest documents”. This at least gives you a starting point to come up with something based on your context.
The only time I’ve had to translate this term, the context let me sidestep it altogether. I could get away with just saying how an official, usually a notary public but sometimes a public servant, would have to certify the document. The text was describing a process, so it was quite easy to get rid of it. It would be more difficult in texts where the term comes up in passing. Although the best approach might still be to sidestep or describe it.
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Hi, Rob,
I agree that there’s not really a snappy rendering for “fe pública” that would fit nicely into a translated text, and a definitional translation will probably have to do in most cases where this can’t be “sidesteped” this as you suggest.
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Rebecca,
My suggestion would also be descriptive: “authority to officially attest to facts occurring in the presence of a public or quasi public official”. Remember that in a civil law system, such as the Mexican system, notaries (who are quasi public officials) no only certify documents signed in his or her presence, but also facts witnessed by the notary at the request on an interested party, so that the ensuing notarial certification may be used in court at a later date by said interested party.
Javier
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Yes, thanks, Javier. That descriptive translation is a mouthful, but there may not be another way to express “fe pública.”
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A shorter alternative could be “official attestation authority,” which will encompass the activities of both notaries and public officials vested with the power to certify documents and also facts occurring in their presence.
Javier
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