The Presbyterian Church (USA), America's largest Presbyterian denomination, voted yesterday to approve same-sex marriage – changing the language of its constitution to deem marriage as between "two people" rather than specifically between a man and a woman.

In a move that one gay-rights activist has described as signifying a "glorious day for the Church," the General Assembly also approved a resolution that will allow pastors to officiate weddings, where state-law allows.

An overwhelming majority of leaders voted to approve the change in definition of marriage, with a landslide of 429 yes votes to 175 no, though regional bodies will now have to approve the decision before it becomes Church policy.

The vote on officiating same-sex weddings won by a narrower margin – 371-238 – though this move needs no further approval and is now embedded in Church law.

Yesterday's resolutions follow the 2011 decision to allow the ordination of gay clergy, but until now ministers were not able to officiate same-sex weddings.

"This is a glorious day for the church and for LGBT people who have been seeking full inclusion here for decades," Rev Randy Bush of the pro-LGBT church group Covenant Network said in a statement.

"We're fully committed to the unity of the Church, and we will do everything in our power to facilitate a denomination that truly welcomes all – including those whose views may differ from the decisions reached by the Assembly today," added his colleague, Rev Brian Ellison, executive director of the Covenant Network.

"We look forward to an ever deeper understanding, not only of marriage but also of our common bonds of faith."

Alex McNeill, executive director of gay advocacy group More Light Presbyterians, also welcomed the move, releasing a statement declaring that Thursday's events were "an answer to many prayers".

"We will keep praying that the majority of our 172 presbyteries will confirm that all loving couples can turn to their churches when they are ready to be married," he said.

However, many conservative members of the Presbyterian Church have expressed their disappointment following the votes, and other denominations within the wider Presbyterian movement remain firmly against same-sex marriage.

The Presbyterian Lay Committee released a statement warning that the Church is turning away from God. "The General Assembly has committed an express repudiation of the Bible, the mutually agreed upon Confessions of the PCUSA, thousands of years of faithfulness to God's clear commands and the denominational ordination vows of each concurring commissioner," it reads.

"This is an abomination. The Presbyterian Lay Committee mourns these actions and calls on all Presbyterians to resist and protest them...God will not be mocked and those who substitute their own felt desires for God's unchangeable Truth will not be found guiltless before a holy God."

Other denominations to signal a move towards full acceptance of same-sex relationships are the Episcopal Church, which has approved blessings for gay marriages, and the Evangelical Lutheran Church in America which allows the ordination of gay clergy. According to The Guardian, the United Church of Christ is the only mainline Protestant denomination to fully support gay marriage, having approved a resolution to support and conduct same-sex weddings in 2005.