ANAHEIM, Calif. — Episcopalians authorized bishops to bless same-sex unions and research an official prayer for the ceremonies yesterday, capping a meeting that moved the church closer to accepting gay relationships despite turmoil over the issue in the Anglican family.

The Episcopal General Convention also underscored the church's desire to remain a full member of the global Anglican Communion. But national assembly's actions are likely to damage the already strained relations within the fellowship.

Delegates voted earlier this week to effectively drop a pledge to act with "restraint" in considering any more openly gay candidates for bishop.

The Episcopal gay advocacy group Integrity said the church "turned an important corner" with the vote.

But the Rev. Dan Martins of the Diocese of Northern Indiana said the measure could widen the rift with overseas Anglicans.

"On this day, my church is covering itself in shame, and I am profoundly sorry for it," he said.

The Episcopal Church caused an uproar among Anglicans in 2003 by consecrating its first openly gay bishop, V. Gene Robinson of New Hampshire. The Anglican spiritual leader, Archbishop of Canterbury Rowan Williams, has struggled ever since to keep the communion unified.

Anglican leaders had pressed Episcopalians for a moratorium on electing more gay bishops, and asked the church not to develop an official prayer for same-gender couples.

But the measure adopted yesterday notes the growing number of U.S. states that allow gay marriages, civil unions and domestic partnerships, and gave bishops in those regions discretion to provide a "generous pastoral response" to couples in local parishes.

The resolution also authorized a church commission to "collect and develop theological resources and liturgies" for blessing same-gender relationships for consideration at the next national convention, in 2012. Many dioceses already allow clergy to bless same-sex couples, but there is no liturgy for it in the denomination's Book of Prayer.

Williams attended the convention's opening and told delegates, "I hope and pray that there won't be decisions in the coming days that could push us further apart."

Back in England, he has said only that he regrets the convention's decision to lift the de facto moratorium on gay bishops. The archbishop of Canterbury does not have the authority to force a compromise, because each Anglican province is independently governed.

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

Presiding Bishop Katharine Jefferts Schori, head of the Episcopal Church, sent Williams a letter, released publicly yesterday, saying that the actions of the convention are not meant to offend and do not mean that any diocese would necessarily consecrate a gay bishop.

"We remain keenly aware of the concerns and sensibilities of our brothers and sisters in other churches across the communion," she wrote. "We believe also that the honesty reflected in this resolution is essential if we are to live into the deep communion that we all profess and earnestly desire."

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

George Wing, a delegate from Colorado, said he worries that the church's liberal direction has caused active churchgoers to leave.

"The problem is, the most dedicated of the young people are evangelicals. They're gone, and they're not coming back," Wing said.