(CNN) -- Episcopal churches in California and Minnesota moved toward appointing gay bishops over the weekend, less than a month after the denomination lifted a self-imposed freeze on promoting openly gay clergy into the top ranks of the church.

Mary Glasspool is a candidate for assistant bishop with the Episcopal Diocese of Los Angeles.

The Diocese of Los Angeles, one of the largest in the country, included a gay man and a lesbian on its short list for assistant bishop positions Sunday.

A day earlier, the Diocese of Minnesota put a lesbian priest on its list of three candidates to lead the statewide religious community.

The nominations seem likely to increase tensions in the 70 million-member Anglican Communion, the world's third-largest Christian community.

The Anglican Communion has been wrestling with how to handle homosexuality, a question that shows signs of tearing the church apart.

The Episcopal Church, as the American branch of the Anglican Communion is known, voted overwhelmingly last month to allow gay men and lesbians to become bishops.

Individual dioceses have moved quickly in the wake of the vote.

Los Angeles announced six candidates for positions as assistant bishops, including Mary Glasspool and John Kirkley, both of whom spoke openly about being gay in statements on the diocese Web site.

Glasspool recalls wrestling in college with the question, "Did God hate me (since I was a homosexual)?"

She refers to her "life partner, Becki Sander," and discusses her discomfort at serving in a "relatively conservative" parish during the 1990s.

"My partner, Becki, was invisible as far as the parish was concerned," writes Glasspool, who is based at the Diocese of Maryland in Baltimore.

Kirkley, rector of St. John the Evangelist in San Francisco, refers to himself as a gay man and is married to a man whom he calls "my husband, Andrew" on the Los Angeles Diocese Web site.

They have an adopted African-American son, he writes, admitting: "It was with some fear and trembling that we two white, gay men embarked upon raising our son."

The head of the Diocese praised all six candidates for the two positions.

"I affirm each and every one of these candidates and am pleased at the wide diversity they offer this Diocese," the Right Rev. J. Jon Bruno said in a statement.

The Los Angeles Diocese has a population of about 70,000 across six southern California counties. It will elect its two new assistant bishops, formally known as bishops suffragan, at a convention December 4-5.

Bonnie Perry, meanwhile, is one of three finalists to become bishop of Minnesota. She has been with her partner, Susan Harlow -- who is also a priest -- for 22 years, she says on the diocese Web site. Perry is currently based in Chicago.

Minnesota Episcopalians will chose their new bishop October 31. More candidates could be added before then.

Five years ago, the Episcopal Church appointed Gene Robinson, an openly gay man, to be bishop of New Hampshire, a move that tore apart the Episcopal Church and prompted a semi-official moratorium on naming new gay bishops.

A number of Episcopal dioceses broke with the official church structure, forming the breakaway Anglican Church in North America in protest of the church's stance on homosexuality.

They say the mainstream Episcopal Church and the aligned Anglican Church in Canada "have increasingly accommodated and incorporated un-Biblical, un-Anglican practices and teaching."

Rowan Williams, the Archbishop of Canterbury and head of the worldwide Anglican Communion, has been trying to bridge the gap between liberals and conservatives on homosexuality.

Last week, he floated the idea that there might be "two styles of being Anglican" in the future.

"The ideal is that both 'tracks' should be able to pursue what they believe God is calling them to be as Church, with greater integrity and consistency," he said in a lengthy statement on his Web site in response to the new Episcopal Church position on homosexuality.

The Episcopalians also moved last month toward blessing same-sex marriages, although they will make no official decisions until their next general convention, three years from now.

Williams denounced anti-gay prejudice but said the Anglican Communion was not in a position to approve same-sex marriages.

"No Anglican has any business reinforcing prejudice against [lesbian, gay, bisexual or transgendered] people, questioning their human dignity and civil liberties or their place within the Body of Christ," he wrote.

But changing the Anglican theological position on homosexuality would have to be "based on the most painstaking biblical exegesis and on a wide acceptance of the results within the Communion," he wrote.

"A major change naturally needs a strong level of consensus and solid theological grounding," he added. "This is not our situation in the Communion."

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