The US Anglican Church is meeting over the next week to discuss a motion to appease Church leaders critical of its gay bishops stance.
The debate comes three years after the Church approved the openly gay Gene Robinson as bishop of New Hampshire, a move that angered conservatives.
Correspondents say the Anglican communion could split if the US body, the Episcopal Church, shuns the motion.
But US Anglicans are not anxious to exacerbate the crisis, they say.
The discussion comes within the framework of a week-long Church convention that ends on 21 June.
'Express regret'
The motion to be discussed suggests exercising "great caution" before ordaining another gay bishop.
It also calls on dioceses to defer same-sex ceremonies until the Anglican communion achieves consensus on the issue.
And it says that the Episcopal Church should apologise "for having breached the bonds of affection in the Anglican communion by any failure to consult adequately with our Anglican partners".
It urges those who took part in Bishop Robinson's election to "express regret" for the pain they have caused.
But it also recognises that gay people are "by baptism... full members of the Church" and apologises to them for years of rejection and maltreatment by the Church.
The motion is mostly based on the recommendations of the Windsor Report, resulting from an inquiry into the row in 2004, although it does not endorse the report's call for a moratorium on consecration.
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