The US Episcopal Church has agreed to "exercise restraint" in consecrating gay bishops in an effort to prevent its expulsion from the Anglican communion.
The election of Bishop Gene Robinson divided Anglicans
The communion has been in turmoil since the 2003 election of the gay bishop Gene Robinson in New Hampshire.
The new resolution is a watered-down version of a proposal, rejected on Tuesday, to stop electing gay bishops.
The compromise will not satisfy traditionalists who regard gay sex as sinful, says the BBC's Robert Pigott.
The traditionalist majority within the Anglican Church had been calling for stricter measures against the ordination of gay bishops.
It had also demanded curbs on church blessings for same-sex couples.
The non-binding resolution, approved on Wednesday at the US Episcopal Church's convention in Ohio, stops far short of meeting their demands.
The resolution says the church must "exercise restraint by not consenting to the consecration of any candidate [for bishop] whose manner of life presents a challenge to the wider church and will lead to further strains on communion".
Earlier, the outgoing Presiding Bishop, Frank Griswold, and the woman who becomes his successor in November, Bishop Katharine Jefferts Schori, had appealed for a compromise.
They called for the convention to show it recognised just how divisive the issue of gay bishops was for Anglicans.
"Unless there is a clear perception on the part of our Anglican brothers and sisters that they have been taken seriously in their concerns, it will be impossible to have any genuine conversation," Bishop Griswold said on Wednesday.
Bishop Schori acknowledged the resolution was "far from adequate" but, she said, "it is the best we can do at this convention".
"This church, the body of Christ, is not wholly one and not wholly two," she said.
Our correspondent says the likelihood of a formal schism within the church depends on the degree to which the compromise offered by the US Episcopals divides the traditionalists who have been calling for their expulsion.
Much of the Anglican communion, dominated by traditionalist churches in the developing world, is unlikely to be satisfied, he says.
The Anglicans' religious leader, Archbishop of Canterbury Rowan Williams, said it was not yet clear how far the resolutions adopted by the Episcopal Church meet demands for a moratorium on gay bishops.
"The wider communion will therefore need to reflect carefully on the significance of what has been decided before we respond more fully," he said on Wednesday.