It has instead asked its local diocese to "exercise restraint" in such appointments.
Delegates at the Episcopal Church's general convention in Columbus, Ohio adopted the motion three days after electing a female leader for the first time in a move that led one diocese to begin the process of leaving the US branch and elicited comments of concern from the world body.
It was weaker than the resolution rejected on Tuesday which asked diocese to "refrain from" ordaining gay bishops or developing rites for the blessing of same-sex unions.
The adopted resolution instead called upon church leaders "to exercise restraint by not consenting to the consecration of any candidate ... whose manner of life presents a challenge to the wider church and will lead to further strains on communion."
Many within the organization hoped it would be sufficient to heal the rift and move towards reconciliation.
It was greeted cautiously by the Archbishop of Canterbury, the religious head of the church.
Homosexuality a sin
Most of the branches of the 77-million strong Anglican Communion around the world have resisted elevating women to bishops and consider homosexuality a sin.
Many severed or restricted ties to the US church, which represents 2.4 million members in the United States and parts of Latin America, after it named an openly gay bishop in 2003.
A report commissioned by the archbishop in response to the rift warned that the Anglican Communion could break apart if the US church does not impose a moratorium until Anglicans worldwide reach a consensus on the issue.
"It is not yet clear how far the resolutions passed this week and today represent the adoption by the Episcopal Church of all the proposals set out in the Windsor Report," Archbishop Rowan Williams said in a statement Wednesday.
"The wider Communion will therefore need to reflect carefully on the significance of what has been decided before we respond more fully."
The election of Bishop Katharine Jefferts Schori as the Episcopal Church's primate and presiding bishop on Sunday was seen by some observers as an additional provocation.
The conservative diocese of Fort Worth, Texas responded by asking the Archbishop of Canterbury to step in and act as its spiritual leader, as it does not believe that women can play that role.
The goal is to eventually set up a separate province in the United States for more orthodox Anglicans, delegation chair Reverend Cannon Charles Hough told AFP.
Several other US diocese and congregations may also join the new province, he added.
"We've got two churches here: one believes in biblical Christianity that's 2,000 years old and the other that believes in feelings and experiences," he said in a telephone interview on Tuesday. "We're not in the same church anymore."
Ms Jefferts Schori is part of the church's liberal majority and backed the ordination of openly gay bishop Gene Robinson in 2003.
She also supports church blessings of same-sex unions but stood behind the resolution urging restraint.