At its annual gathering in June, the church took the decision not to allow those in same-sex relationships to be full members.
This includes denying baptism to the children of gay couples.
The church also decided not to send its moderator to the Scottish General Assembly, nor invite its leader to the annual Belfast General Assembly because of that church's more liberal attitude to same-sex marriage.
This week 232 senior members of the Presbyterian Church in Ireland signed a letter expressing their "profound sense of hurt, dismay and anger" at those decisions.
"This level of feeling is unprecedented in our pastoral experience," they said.
"We are committed to doing all we can to ensure that the decisions which have prompted such a level of concern will be subject to the urgent attention they deserve, and for which many in the church are calling.
"We gladly acknowledge that we ourselves have been constantly enriched and challenged by the diversity of views found in the Presbyterian Church in Ireland.
"Therefore, as we participate in this work of critical engagement and discernment, we hold that any unnecessary narrowing of the range of acceptable theological perspectives within the Presbyterian Church in Ireland will damage our credibility and limit our future."
The letter concluded: " We make this statement: as a prayerful expression of appropriate loyalty to the Presbyterian Church in Ireland at this moment in our history; as a necessary consequence of our ordination vows, which we take with the utmost seriousness; and by the grace of God, as an imperfect yet credible witness to our trust in Jesus Christ alone."
Last month, former Stormont Speaker Lord Alderdice quit the church over concerns at those decisions.
He resigned both as an elder of the church and a member.
The former Alliance Party leader said he had been concerned by the "trajectory" the Presbyterian Church had been on for quite some time.
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