A landmark vote saw the largest Presbyterian denomination in the US change the wording in its constitution to approve same-sex marriage yesterday.

The marriage contract is now explicitly referred to by the Presbyterian Church (USA) as  "between two people, traditionally a man and a woman" rather than merely "between a man and a woman".

An overwhelming majority of church leaders voted to approve the change in definition last year, but regional bodies had to approve the decision before it became church policy. Yesterday, the majority of the 171 presbyteries voted in favour of the change.

In a video message on the Presbyterian Church (USA) website, church official Gradye Parsons confirmed that Tuesday's vote will allow Teaching Elders "wider discretion in whose weddings they may conduct," including same-sex couples.

However, no church leaders will be compelled to conduct a wedding against their judgement, Parsons said. He encourages members to show "respect and genuine care for each other," regardless of differing views on the subject.

"As a church the Presbyterian Church (USA) has received much grace from God in Jesus Christ. We should extend that grace to each other in all gentleness as we live into this chapter of our common life," he added.

Rev Randy Bush of the pro-LGBT church group Covenant Network said yesterday's vote signifies the church stepping "forward into a new chapter – one that values our past journeys of faith [and] respects the importance of pastoral discretion in congregational matters".

"[It] offers to the world a compelling witness about how God's grace is active in loving, mutual relationships," he said.

"The change aligns the church's constitution with a reality that has long been true: Both same-gender and opposite-gender couples have been living in relationships that demonstrate covenant faithfulness, shared discipleship, and mutual love," a statement from the Covenant Network said.

"We rejoice that all couples can now see those relationships solemnized before God and the Christian community in marriage, at the discretion of ministers and sessions."

Presbyterian Church (USA) has around 1.8 million members. The General Assembly approved a resolution in 2011 to allow lesbian and gay leaders in the church, and last year voted to allow pastors to officiate same-sex weddings, where state law allows.

According to the Washington Post, the church has lost 37 per cent of its membership since 1992, which many attribute to disputes over gay marriage. The national director of conservative group The Fellowship Community, Paul Detterman, said more people are likely to leave over this latest decision. However, he said that he and others have chosen to stay "because we believe God has called us here."

"We disagree with the outcome of the vote, but our voice is still welcomed in this denomination, and as long as that is the case we have the opportunity to share the Good News of Jesus Christ here," Detterman told Christian Today.

A statement from The Fellowship Community said that the church was "disregarding the clear teaching of Scripture, the wisdom of those who have lived and died for the faith before us, and the continuing consensus of the contemporary church around the world."

"To do this is both diso-bedient and unwise," the statement continued. "We know this particular change was intended by its proponents to extend the grace and the good news of Jesus Christ, and to further the witness of his Kingdom. We believe it accomplishes neither."