Arson experts are investigating suspicious fires at three Melbourne churches with links to child sex abusers.

Police say they don't believe there's a connection between the blazes but will examine any similarities amid speculation they might have been vigilante attacks.

The Catholic churches at Brighton, St Kilda East and Dandenong each have links to known and alleged pedophile priests.

Regional Bishop Peter Elliott says security is being increased within the Melbourne Archdiocese but doesn't think there's a link between the fires and each church's history.

"I would suggest it rests in a very disturbed mind of an arsonist that likes burning churches," Bishop Elliot told Fairfax Radio on Wednesday.

The most recent blaze at a Dandenong church early on Wednesday was put out before major damage could be done.

Detective Senior Constable Nic Hayes says there is nothing to suggest a connection so far at the site.

"There is nothing to suggest they are linked - just that they are churches," Det Sen Cons Hayes told reporters.

The Dandenong church is linked to Kevin O'Donnell, a former priest, who spent 15 months in jail for indecently assaulting 10 boys and two girls, aged between eight and 15.

A suspicious blaze destroyed St James Church in Brighton early on Monday, while St Mary's Church in St Kilda East also received minor damage from a fire police believe was deliberately lit.

Both churches were attended by notorious priest Ronald Pickering.

Pickering, now dead, was accused of child sex abuse against a number of boys in the 1970s and 1980s but was never convicted.