In her first opening address to the General Convention of The Episcopal Church in the US, the Most Rev Katharine Jefferts Schori made it very clear that the denomination she presides over is in the middle of a crisis.

“The crisis of this moment has several parts,” the US Episcopal leader remarked at the opening of her denomination’s primary governing and legislative body on Tuesday.

And the overarching connection in all of these crises, she continued, has to do with “the great Western heresy – that we can be saved as individuals, that any of us alone can be in right relationship with God”.

But, as the theme of the convention – “Ubuntu” – implies, “selfishness and self-centredness cannot long survive”, she said.

“We are our siblings’ keepers and their knowers, and we cannot be known without them – we have no meaning, no true existence in isolation,” she added.

Jefferts Schori’s address was delivered as The Episcopal Church continues its struggle to keep its members united following the divisive election of the denomination’s first openly gay bishop, Gene Robinson of New Hampshire.

Since Robinson's 2003 consecration, a number of churches have withdrawn completely from both The Episcopal Church and the wider Anglican Communion to form their own Anglican jurisdictions. Others have withdrawn from The Episcopal Church but aligned with other bodies within the Anglican Communion.

Last month, around 700 breakaway parishes in North America officially united into a single church body – the Anglican Church in North America – that is meant to serve as an orthodox Anglican, mission-minded, and biblically-centred province. Together, the parishes represent some 100,000 conservative Anglicans.

Though never directly mentioning critics of The Episcopal Church, Jefferts Schori noted that “some quarters” insist that “salvation depends on reciting a specific verbal formula about Jesus”.

“The temptation for us here will be to see one small part of God’s mission, the part each one of use holds most dear, as the overarching reason for this Church’s existence. The reality is that God’s mission will continue, whatever we do here, but it may not advance as effectively or penetrate as widely in the next few years if we get selfish or miss the mark,” she said.

Furthermore, she added, there are aspects of mission that are more appropriate and effective at the congregational and diocesan level.

“We might also consider putting in that category the big picture issues we can’t yet agree on – the ones for which we have many, more local, and varied understandings, recognising the different contexts may require different responses,” she added, possibly suggesting that congregations should be allowed to decide individually on the issue of homosexual clergy and same-sex unions as the Presbyterian Church (PCUSA) voted to do.

Episcopal leaders at this year's convention, which takes place in Anaheim, California, will be considering resolutions that would allow the consecration of openly gay bishops. Some dioceses, or regional bodies, have asked the General Convention to repeal or retract B033, a resolution passed in 2006 that calls for restraint in ordaining bishops "whose manner of life presents a challenge to the wider church" – mainly noncelibate homosexuals.

One new resolution that will be introduced and debated at this week’s General Convention will seek to extend a key marriage ritual to gay and lesbian couples, particularly in the six states that recognise same-sex marriages – Massachusetts, Maine, Vermont, New Hampshire, Iowa and Connecticut.

"In all six states, faithful Episcopalians are asking that their church provide the pastoral support and blessing of the church for their marriages," reads an explanation attached to the resolution. "Clergy in those same states are caught between the authority given them by the state and the discipline of The Episcopal Church as it's currently described."

Anglican leaders overseas, however, have warned The Episcopal Church against rescinding resolution B033 this year or passing any resolution that would "imperil" the future of the Anglican Communion.

In her opening address Tuesday, Jefferts Schori reminded the General Convention that its triennial gathering is always a time of critical decision-making.

“The decision-making we face here is an opportunity to choose the direction of our journey into God’s mission,” she said.

“We will fail if we choose business as usual,” the presiding bishop added.

This week’s General Convention, the 76th, comes months after the Anglican Consultative Council, a decision-making body of bishops, clergy and laity, reaffirmed the moratoria on the consecration of partnered gay bishops and the authorisation of public rites blessing same-sex unions.