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In one of several emotional appeals for passage, Pete Ross, a lay delegate from the Diocese of Michigan, described an earlier hearing on same-sex blessings when a man spoke about his lifelong male partner, who had recently died.

“He told us the anniversary they celebrated in their relationship was when they signed their mortgage,” Mr. Ross said, choking back tears. “It’s time for our church to honor these lifelong commitments.”

The official liturgy for same-sex blessings has been in development since 2009, when it was authorized by the last General Convention. Some bishops already had created rites for the ceremonies for use in their own dioceses, but the prayers approved Tuesday are the first such official prayers for use by the entire church, which claims just under 2 million members.

The liturgy can be used starting Dec. 2, the first Sunday in Advent.