Under the compromise approved on a 104-30 vote with two abstentions, bishops who oppose gay marriage are not obligated to extend their blessings, The New York Times reported.
However, the church's bishops will work on collecting and developing "theological and liturgical resources" for same-sex blessings and report back at the next convention in three years, the Times said.
"It's a big step forward," said Bishop Thomas C. Ely of Vermont.
The compromise wording says bishops in states where same-sex marriage, civil unions or domestic partnerships are legal "may provide generous pastoral response to meet the needs of members of this church."
The measure will now go to a church body representing the clergy and lay members, which is expected to approve it at the convention this week.
Episcopal conservatives, such as the Rev. Steve Wood of St. Andrews Church in Mount Pleasant, S.C., said those opposed to gay marriage "are treated more as zoological oddities."
"We're patted on the head, nice-nice, and then we get steamrolled," Wood said.
The gay marriage blessing vote followed one on Tuesday in which the bishops approved language allowing the ordination of more openly gay bishops.
It remains to be seen whether the votes this week in Anaheim will lead to permanent schism in the Anglican Communion.
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