ANAHEIM, Calif. — Episcopal bishops authorized the church Wednesday to start drafting an official prayer for same-sex couples, another step toward acceptance of gay relationships that will deepen the rift between the denomination and its fellow Anglicans overseas.

The bishops voted 104-30 at the Episcopal General Convention to “collect and develop theological resources and liturgies” for blessing same-gender relationships, which would be considered at the next national meeting in 2012.

The resolution notes the growing number of states that allow gay marriage, civil unions and domestic partnerships, and gave bishops in those regions discretion to provide a “generous pastoral response” to couples in local parishes.

Many Episcopal dioceses already allow clergy to bless same-sex couples but there is no official liturgy for the ceremonies in the denomination’s Book of Prayer. The measure still needs the approval of the lay people and priest delegates at the assembly, which ends Friday.

“We certainly feel a deep need to be able to proclaim the love of God in the midst of a changing reality,” said Suffragan Bishop James Curry of the Diocese of Connecticut, one of six states that are legalizing same-gender marriage.

A day earlier, the convention had declared gays and lesbians eligible for “any ordained ministry,” even though Anglican leaders had sought a clear moratorium on consecrating another gay bishop. The vote effectively lifted a self-imposed Episcopal pledge from three years ago to use “restraint” in approving another bishop in a same-sex relationship.

The Episcopal Church caused an uproar in 2003 by consecrating the first openly gay bishop, V. Gene Robinson of New Hampshire.

To calm tensions and keep the global Anglican Communion, Anglican leaders five years ago pressed Episcopalians for a temporary ban on electing gay bishops, and asked that the church refrain from developing an official prayer service for same-sex couples.

At the start of the convention last week, the Anglican spiritual leader, Archbishop of Canterbury Rowan Williams, told delegates, “I hope and pray that there won’t be decisions in the coming days that could push us further apart.”

A spokeswoman for Williams said Wednesday that he would not comment.

The 77 million-member communion is the third-largest grouping of churches worldwide, behind Roman Catholic and Orthodox Christian churches.

Most overseas Anglicans believe Scripture bars same-sex relationships and disagree with how liberals interpret the Bible on a wide range of issues. Liberal Anglicans emphasize biblical social justice teachings and believe their fellowship can contain conflicting views.

Last month, breakaway Episcopal conservatives and other like-minded traditionalists formed a rival national province to the Episcopal Church called the Anglican Church in North America.

The new body includes four seceding Episcopal dioceses and is supported by several overseas Anglican leaders who have broken ties with the Episcopal Church.

Episcopal conservatives who have stayed with the denomination lamented the latest votes and predicted the already splintering Anglican fellowship would fracture.

“For many, this is the final straw with members of the wider Anglican Communion,” said Bishop William Love of Albany, N.Y. “It’s breaking my heart to see the church destroy itself in the manner in which we seem to be doing.”