Compared with previous General Assemblies, “this has felt completely different,” said Alex McNeill, a candidate for ordination and the executive director of More Light Presbyterians, a group advocating gay equality in the church. “There is such a sense of growth and mutual respect across the theological spectrum.”

But it deeply pained those Presbyterian commissioners in the church’s conservative wing, who warned that congregations that have been on the brink of departure would leave.

“My heart breaks,” the Rev. Steve Wilkins, representing the New Harmony Presbytery in South Carolina, said during the debate. “I don’t think it’s up to us to change the definition of marriage; in fact marriage has been defined by us and revealed to us in God’s word.”

About 350 of the denomination’s congregations have left since 2010, when the General Assembly voted to ordain openly gay clergy members, said the Rev. Gradye Parsons, the church’s stated clerk, in an interview. But it is still the nation’s largest Presbyterian denomination, with 10,038 churches in 2013 and about 1.8 million members.

On the measure to allow the clergy to perform same-sex marriages, the vote of the 565 commissioners was 61 percent in favor, and 39 percent opposed.

The Rev. Jeffrey Bridgeman, pastor of El Montecito Presbyterian Church, in California, served as the moderator of the 71-member committee that voted overwhelmingly to endorse both resolutions, even though, personally, he is opposed to same-sex marriage. He said in an interview before the vote that 10 of the 33 churches in his presbytery had left in the past two years, but that his quite conservative church was staying for now because “they feel they have a ministry.”

The assembly also passed a resolution to undertake a churchwide “reconciliation” effort to reach out to congregations that disagree with these decisions but want to remain in the denomination. But church leaders said they had no concrete plans yet for how the church could promote reconciliation in the next year while each presbytery must debate and vote whether to ratify changing the definition of marriage in the Book of Order.