Nigeria's Anglican Church says the US branch of the church is "a cancerous lump" that should be "excised".
Nigerian Archbishop Akinola can boast a following of 17.5 million
Nigerian bishops were responding to a proposal from the Archbishop of Canterbury Rowan Williams last week.
He had suggested the introduction of a two-tier system of church membership to avoid complete disintegration over the issue of homosexuality.
The US branch, known as the Episcopal Church, outraged conservatives by consecrating gay Bishop Gene Robinson.
There have also been disagreements surrounding church blessings for same-sex couples.
Division, not schism
Dr Williams has been attempting to straddle the bitter divisions, and last week proposed a solution.
He suggested that the Anglican Communion, which is the loose network of individual Anglican churches around the world, could be divided into "associated" and "constituent" provinces.
Under this system, the Episcopal Church would accept a lesser role to avoid a schism with the majority of more conservative churches.
Dr Williams urged both sides to heed the need for change, arguing that: "Neither the liberal nor the conservative can simply appeal to a historic identity that doesn't correspond with where we now are."
In their statement, posted on two websites, the Nigerian bishops commend Dr Williams' idea as "brilliant as the heartbeat of a leader who wants to preserve the unity of the Church by accommodating every shred of opinion no matter how unbiblical".
But they dispute whether the challenge is really to "fashion out a novel establishment that is elastic enough to accommodate all the extremes of the referred modes of expression of the same faith".
"A cancerous lump in the body should be excised if it has defied every known cure," they say.
"To attempt to condition the whole body to accommodate it will lead to the avoidable death of the patient."
Instead Dr Williams should persuade churches that chose to "walk apart" to "return to the path", say the bishops.
The Nigerian Anglican Church is Africa's largest Anglican church, with an estimated 17.5 million members.
It has led traditionalist attempts to expel the Episcopal Church and, according to the BBC's religious affairs correspondent, Robert Pigott, has even hinted that it might have to take over from England the role of leading a truly Bible-believing Communion.
Our correspondent says this statement is a sign of their intent to lead other Anglican churches in opposition to the Americans at a meeting of what is known as the Global South in September - and perhaps at a meeting of all 38 autonomous Anglican churches next February.