After an emotional debate over the authority of Scripture and the limits of biblical inclusiveness, leaders of the country’s largest Lutheran denomination voted Friday to allow gay men and lesbians in committed relationships to serve as members of the clergy.

The vote made the denomination, the Evangelical Lutheran Church in America, the latest mainline Protestant church to permit such ordinations, contributing to a halting sense of momentum on the issue within liberal Protestantism.

By a vote of 559 to 451, delegates to the denomination’s national assembly in Minneapolis approved a resolution declaring that the church would find a way for people in “publicly accountable, lifelong, monogamous same-gender relationships” to serve as official ministers. (The church already allows celibate gay men and lesbians to become members of the clergy.)

Just before the vote, the Rev. Mark Hanson, the church’s presiding bishop, led the packed convention center in prayer. When the two bar graphs signaling the vote’s outcome popped up on the hall’s big screens seconds later, there were only a few quiet gasps, as delegates had been asked to avoid making an audible scene. But around the convention hall, clusters of men and women hugged one other and wept.