This latest protest, which the Baptist and Uniting churches have also joined, takes a different tack to previous objections, said the Sydney Morning Herald.
The Anglican church has so far argued children absorb ethics through the school curriculum and do not need the subject to be taught separately.
Jude Hennessy, the director of the Confraternity of Christian Doctrine for the Wollongong diocese and co-ordinator of the campaign, said: "We would love ... if the government thought that ethics were a worthwhile addition to the curriculum, to enable Catholic kids to have the opportunity to attend it.
"It is not fair they should miss this opportunity. Nor is it fair their parents should be caught in a dilemma about whether to send them to formation in their faith tradition or to choose ethics."
Mr Hennessy said the petition, which has more than 35,000 signatories, was intended to recognise "the important place ethics plays in state schools".
"It simply asks that if ethics classes are regarded as a valuable addition, they be run at a time other than during SRE time."
SIC: CTHAUS