SALT LAKE CITY — Episcopalians voted overwhelmingly Wednesday to allow religious weddings for same-sex couples, solidifying the church’s embrace of gay rights that began more than a decade ago with the pioneering election of the first openly gay bishop.

The vote came in Salt Lake City at the Episcopal General Convention, just days after the U.S. Supreme Court legalized gay marriage nationwide. It passed in the House of Deputies, the voting body of clergy and lay participants at the meeting. The House of Bishops had approved the resolution Tuesday by 129-26 with five abstaining.

The Very Rev. Brian Baker of Sacramento said the church rule change was the result of a nearly four-decade long conversation that has been difficult and painful for many. Baker, chair of the committee that crafted the changes, said church members have not always been kind to one another but that the dynamic has changed in recent decades.

“We have learned to not only care for, but care about one other,” Baker said. “That mutual care was present in the conversations we had. Some people disagreed, some people disagreed deeply, but we prayed and we listened and we came up with compromises that we believe make room and leave no one behind.”

Baker said the House of Bishops prayed and debated the issue for five hours earlier this week before passing it on to the House of Deputies.