A group of evangelical churches has been accused of running scared after it called on the Scottish Episcopal Church to retract a statement on gay priests.
Openly gay Gene Robinson was ordained in the US last year
The church's College of Bishops said that being a practising homosexual was not a bar to ordained ministry.
The Scottish Anglican Network warned it will consider breaking away unless the church changes its stance.
Changing Attitude Scotland accused the evangelical group of being "frightened" of a discussion on the issue.
Changing Attitude Scotland is a network working for the "full affirmation" of lesbian and gay people in the church.
It said there had been a "huge expression of support" for the bishops' statement.
Its convener, the Reverend Kelvin Holdsworth, said the bishops had called for discussion between those of different views.
"Those who are calling for the bishops to withdraw their statement appear to be frightened of that discussion taking place," he told BBC Scotland's news website.
SCOTTISH EPISCOPAL CHURCH
Member of the worldwide Anglican Communion
An estimated 45,000 members
Autonomous and rooted in the pre-Reformation church in Scotland
Adopted the 1637 Scottish Book of Common Prayer
Persecuted following the 1715 and 1745 Jacobite uprisings
Theological College founded in Edinburgh in 1810, the first in the Anglican Communion
General Synod established in 1982
Ordained first Episcopalian woman priest in 1994
Passed motion allowing woman bishops in 2003
"Members of Changing Attitude Scotland are looking forward to engaging in the dialogue which the bishops propose.
"We particularly enjoy discussing the authority of scripture and the ways in which we understand the Bible to be consonant with the view that gay people in relationships can live open godly lives within the Christian faith."
The controversy over the statement, which was posted on the church website earlier this month, began last week.
The Scottish bishops said the church "had never regarded the fact that someone was in a close relationship with a member of the same sex as in itself constituting a bar to the exercise of an ordained ministry".
The evangelical Scottish Anglican Network has written to all bishops voicing its concern - and is threatening to reconsider its position within the denomination if it does not get a swift response.
The Reverend David McCarthy, rector of St Silas Church in Glasgow, said the statement was "a move away from what the Bible teaches us".
He told BBC Radio's Good Morning Scotland programme: "This weekend there have been a number of people in my congregation who are just appalled by what the church has been saying in the past few days."
He said the network had received messages of support from around the world.
He said the churches did not want to "up sticks and leave", but warned: "The bishops have placed us in a situation where there is a split that's going on.
"There are two different ways of seeing the gospel, but that being the case there will have to be some kind of action that would reflect that we don't agree.
"We would see ourselves as being in the long-standing tradition of Scottish Episcopalianism. We would be the ones holding on to orthodoxy."
The network's Reverend Canon Philip Noble added: "The American church have now taken a step back from their extreme position, so I fear that we as an Episcopal church might be the most extreme of all the churches in the world at the moment."
A meeting between the Scottish Anglican Network and the church has been arranged for early next month.