Short answer. Not by yourself, and not through the registrar alone. If an impediment is brought to the local civil registrar's attention, he notes it in the application — but shall nonetheless issue said license after the publication period, unless ordered otherwise by a competent court. Stopping the license takes a court order.
What the law says
he shall note down the particulars thereof and his findings thereon in the application for marriage license, but shall nonetheless issue said license after the completion of the period of publication, unless ordered otherwise by a competent court
Family Code, Article 18 — Registrar's Notation of a Known Impediment. Read the full provision →
The registrar records — he does not refuse
The Family Code deliberately gives the local civil registrar a narrow role. Where an impediment is known to the local civil registrar or brought to his attention, his duty is documentary: he shall note down the particulars thereof and his findings thereon in the application for marriage license. What he cannot do is turn your report into a refusal — the provision continues that he shall nonetheless issue said license after the completion of the period of publication. The registrar is not a judge of impediments; reporting to him creates a paper trail, not a roadblock.
The court is the only stop sign
The license is withheld only when a competent court so orders — and the provision names who can set that in motion: the court may act at his own instance or that of any interest[ed] party. So the person who knows of the impediment does not merely whisper to the registrar and hope; an interested party can go to court and ask for an order directing the registrar not to issue the license. The registrar himself may also bring the matter to court. Until such an order exists, the publication period runs and the license issues on schedule — which is why timing is everything in this situation.
The law removes the cost excuse
The provision ends with a detail that tells you the law wants genuine impediments raised: No filing fee shall be charged for the petition nor a corresponding bond required for the issuances of the order. Petitioning the court to withhold a marriage license costs no filing fee, and the petitioner is not made to post a bond. Compare that with ordinary litigation, where fees and bonds are the norm, and the message is clear — a person with real knowledge of a real impediment should not be priced out of bringing it before a judge.
What to do, concretely
First, report the impediment to the local civil registrar where the application was filed, in writing, with whatever proof you have — an existing marriage certificate, a birth certificate showing the parties' relationship, or similar documents — so the notation is made. Second, if the wedding must actually be stopped, see a lawyer at once about petitioning the court before the publication period ends, since the registrar will otherwise issue the license. Be ready to substantiate what you claim: an impediment is a legal conclusion built on facts, and the court will act on evidence, not on suspicion. If the license issues before anything is done, the question shifts to the validity of the marriage itself.