The vote in the Houses of Bishops and Deputies was more than two-thirds in favor and one-third opposed or abstaining.

The House of Bishops also took up a measure that would create a liturgy to bless same-sex couples. Such blessings are already being done in many dioceses, without official sanction. “It is time for our church to be liberated from the hypocrisy under which it has been laboring,” Bishop Stacy Sauls of Lexington, Ky., told his fellow bishops on Tuesday.

Image The Episcopal Churchs first openly gay bishop, V. Gene Robinson, at the convention Monday. Credit... Chris Pizzello/Associated Press

The Episcopal Church acted despite a personal address at the start of the convention from the Archbishop of Canterbury, Rowan Williams, who as head of the Church of England is considered “first among equals” among the communion’s archbishops. “Along with many in the communion,” the archbishop said, “I hope and pray that there won’t be decisions in the coming days that will push us further apart.”

The resolution passed Tuesday was written in a way that would allow dioceses to consider gay candidates to the episcopacy, but does not mandate that all dioceses do so. It also emphasizes that the Episcopal Church has “an abiding commitment” to the Anglican Communion.

It says that many gay men and lesbians are already ministering in the church and that “God has called and may call such individuals, to any ordained ministry in the Episcopal Church, and that God’s call to the ordained ministry in the Episcopal Church is a mystery which the church attempts to discern for all people through our discernment processes acting in accordance with the constitution and canons of the Episcopal Church.”

Pamela Reamer Williams, a spokeswoman for Integrity USA, an advocacy group for lesbian, gay, bisexual and transgender members of the church, said: “The church has stated very clearly that all levels of the ministry in the Episcopal Church are open to the L.G.B.T. baptized. It is a change in the sense that it supersedes the effective moratorium.”