Rather than trying to protect marriage as a religious institution, the church says people should object on the grounds that same-sex marriage is "against the natural order."
The Sydney Archdiocese, the Knights of the Southern Cross and the Catholic Women’s League sent out an open letter urging Catholics to contact their MPs.
The letter states: “Marriage between a man and a woman is not a religious construct but a natural institution found across all cultures and religions. Marriage is a unique kind of sexually complementary union with a natural orientation to life.”
It also says married heterosexual couples who are infertile still have more right to marriage because “their lovemaking is designed to give life”.
“Allowing two men or two women to marry would involve a fundamental change in our understanding of marriage, from a life-giving and sexually complementary union to a personal, romantic relationship with no true communion or connection to procreation,” the letter reads.
Equal marriage advocates have written to Cardinal George Pell seeking a meeting to explain their point of view and end the negative campaign.
Australian Marriage Equality spokesperson Peter Furness said the church would still be free to choose who they did and did not marry.
"Just as the Church may refuse to marry divorced partners, even though they can marry under civil law, so the Church will still be able to turn away same-sex partners, even when the law is changed to allow us to marry," Furness said.
"We want a meeting with Cardinal Pell to ask him to respect the right of same-sex couples to marry under civil law in the same way we respect the right of the Catholic church not to marry same-sex couples."
Furness said the Church's campaign was a breach of the separation of church and state, was divisive and could lead to greater prejudice against LGBTI people.
"Many Catholics will rightly wonder why the Church instructs them to lobby against two people making a lifelong commitment, when poverty, war and the plight of refugees remain such critical local and global issues," Furness said.
"This kind of anti-equality campaign will inevitably incite discrimination and prejudice against GLBT people, with a particularly negative impact on young people and those in the Church."
AME has launched its own campaign to urge supporters of same-sex marriage to lobby their local MPs in favour of reform.
Furness said part of the campaign was to "emphasise that heterosexuals of different faiths or no faith are allowed to marry, as are heterosexuals who cannot have children."
"Why should there be a different standard for same-sex partners?" he said.