Cardinal Timothy Dolan says the church hasn't "been too good at that" and could work on being more welcoming to gays and lesbians.
He says the church tries its "darnedest to make sure we're not an anti-anybody."
Dolan made the remarks Sunday on the ABC News program "This Week."
His comments came days after the Supreme Court heard arguments in two same-sex marriage cases.
Dolan says he would tell gay men and lesbians that God loves them and they're entitled to friendship. But he says marriage is a union between a man and a woman "where children can come about naturally."
Dolan made similar comments on CBS' "Face the Nation."