Terry Prendergast of Marriage Care, which is partly funded by the Church, said there was no evidence children were harmed by having same-sex parents.
But the organisation representing Catholic bishops said children need parental role models of both genders.
It said Mr Prendergast, a former priest who has since married, was wrong.
Mr Prendergast made his comments to a gathering of gay Roman Catholics in Leicester.
He told the audience at the Quest conference that same-sex families, along with single and cohabiting parents, suffered discrimination and denigration because they fell short of the Vatican's definition of what constituted a real family.
Instead, he said, they should be held up as role models and an advert for Catholicism.
Mr Prendergast also claimed that there was no evidence to show that children of same-sex parents suffered in any way, and that the elements that made for successful child-rearing were stable relationships.
But the Catholic Bishops Conference of England and Wales has insisted that Mr Prendergast is wrong.
Pastoral response
In a statement, the organisation acknowledged that although it was difficult to define what a family was, the Church still believed that stability for children came from having parents of opposite genders who could provide different role models.
They said it was "inconsistent with Catholic teaching to plan or promote a notion of family from which (these elements) .... are deliberately excluded."
Marriage Care provides counselling and support for family relationships and marriage preparation through a network of volunteers and a telephone helpline.
It grew out of Church's pastoral response to couples who were experiencing problems in their marriage.
Many of the organisation's regional centres are funded in part by donations from Catholic dioceses.
The head of the Catholic Church in England and Wales, Archbishop Vincent Nichols, is a strong opponent of gay adoption, and fought an unsuccessful campaign to allow Catholic adoption charities to be exempted from equality legislation which outlawed discrimination against homosexual adoptees.
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