The Evangelical Fellowship of Irish Clergy (EFIC) said he should consider his position on the issue after he said that the Church may need to give a "new status for homosexual relationships" if science proves people are gay.
The fellowship is made up of between 70 and 100 mostly junior Northern Ireland clergy who want a more conservative theological approach.
In a letter to the Belfast News Letter published at the weekend, the fellowship said Archbishop Harper's comments "contradicted the Church of Ireland's own position". It added, "we are dismayed at the lack of clarity and the resulting confusion of the archbishop's approach to human sexuality, especially homosexuality.
"We are painfully aware that this issue has the potential to rip the fabric of the Anglican Communion apart . . . and we are distressed that the archbishop should inflame divisions even further."
One of the fellowship's more vocal members Rev Clive West has said the church needed to go through a "second Reformation".
Archbishop Harper referred the fellowship to the pastoral letter issued by the Church of Ireland bishops in September 2003 on same-sex issues, which "both affirms the centrality and authority of the scriptures for all Christian discourse and sets out the range of views on human sexuality held within the Church of Ireland".
He affirmed "that the scriptures contain all things necessary for salvation" and noted that "the bishops' letter also encourages an attitude of respect for one another and indicates that the church is in a period of active listening on the issue of human sexuality".
He drew attention "to the established principles within Anglicanism of using scripture, tradition and reason in coming to agreed understandings", and pointed out that "the Church of Ireland does not have any provision for the blessing of same-sex relationships and it defines marriage as between one man and one woman".
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