An investigation into recent and historical sex offences is under way in Gwynedd.
North Wales Police said it was aware of rumours circulating in the community regarding the Criccieth Family Church and the "impact this may be having".
A 43-year-old man, a former member of the evangelical church, has been arrested and released on bail.
Det Supt Gareth Evans said: "The enquiry is both sensitive and complex and will take weeks to complete."
The force said there were no ongoing risks but said anyone affected in any way could contact them by emailing or calling 101 and quoting Operation Blue Quartz.
He added: "We have a team of specialist officers dedicated to the enquiry who are working with the safeguarding team from the church and our partners in local authorities.
"I would like to reassure our local communities that there are no ongoing risks you need to be worried about."