Archbishop Harper was speaking at the Anglicans in World Mission conference
The head of the Church of Ireland has said if homosexuality is proven to be biologically predetermined then his church would have to allow gay unions.
"If such comes to be shown, it will be necessary to acknowledge the full implications of that new aspect of the truth," said Archbishop Alan Harper.
His remarks come in the wake of the recent controversy surrounding comments made by DUP MP Iris Robinson.
Mrs Robinson said that gay sex was a sin and an abomination.
Alan Harper, who was speaking at the Anglicans in World Mission conference in Swanwick, England, called on members of the church to return to the core principles of the faith in order to resolve the controversy over gay marriages.
Mr Harper also said it was important to distinguish parts of the Bible that were considered the direct word of God and other elements that were human interpretations of his teachings in the context of the time.
"Rulings that may have applied and been deemed valid at one time and in one specific circumstance need not necessarily retain that applicability and validity at another," he said.
The primate said it was time for a reasoned debate on the issue of homosexuality.
"It is no exaggeration to say that the debate within Anglicanism on the place of homosexuality in human society and the relationship of homosexual acts to the law of God has become deeply visceral and that the quality of debate has suffered as a result," he said.
A spokesman for the Church of Ireland said: "The archbishop's address draws no parallels between same-sex relationships and marriage.