Gender is really not an issue, she said in a phone conversation a fortnight ago, just before travelling to the UK to preach at the annual pilgrimage in St Albans. "It's been a very minor theme. When I was first elected, there was profound objection from a couple of bishops who did not think that women should be ordained. We've long ago gotten past that: they decided they didn't want to be part of the Episcopal Church.

"My gender is really beside the point. I think it was more significant for the Episcopal Church that I was the first scientifically trained Presiding Bishop, and the first Presiding Bishop who was elected from the Western part of the US; and I'm probably the first one who was elected not having spent one's whole adult life in the Church as a primary vocation."

KATHARINE JEFFERTS was brought up as a Roman Catholic until she was eight. Her first encounter with a woman priest was at graduate school, when she was studying oceanography. "I began attending church regularly, and there was a deaconess who'd been in the diocese of Oregon for some time. She was the first woman ordained there, and she was ordained in the parish I attended."

It was only some years later, after a scientific career and marriage to Richard Schori, a mathematician, that she considered ordination - in answer, she says, to the urging of others.

She did her first year of theological training at a Roman Catholic Benedictine seminary. "A number of the fellows there thought I was from Mars [Venus, surely?], but there were several who were very supportive, and several in the faculty of the monks were supportive. It's always been a mix." She became Presiding Bishop after five years as Bishop of Nevada.

Speaking in the run-up to the General Synod vote, she commiserates with women priests in the Church of England.

"It's been an exceedingly difficult and long road. There is really no theological justification for dividing access to ordination as a priest and ordination as a bishop. It was very unfortunate that the Church of England took that decision to divide them early on."

She recalls a visit to Salisbury, where she met a group of parishioners. "After an afternoon's conversation, one of the men said to me: 'I can't imagine taking orders from a woman bishop.' I pointed out to him that that was not the primary role of a bishop, and, at the same time, the head of his Church has been a woman for a very long time."

In her experience, there remains a "cultural aversion, deeper than rationality", that has blocked women from the priesthood, and continues to hinder their appointment to senior posts. "There's a maxim that people may not agree with the idea of a woman priest, or of this kind of a priest, or of that kind of a bishop - but when they need one, and experience the ministry of a person in that role, they usually get past that."

She acknowledges that there is still ground to make up in the United States. "There is canonical equality," she says, "but not equal access. The number of senior women - bishops, deans - does not represent the presence of women as priests."

She thinks that the UK might eventually move faster than the Episcopal Church in the US, since priests and senior clergy are appointed to posts, not elected, as in the US. "I think you're more fortunate in the UK, in that you don't elect your bishops."

Since her election as Presiding Bishop in 2006, unity between the Anglican Primates has been strained. Whether any of this has been on account of her sex cannot be judged. The chief issue has been her Church's support for gay priests and, in particular, the election of the Rt Revd Gene Robinson, a gay man with a partner, as Bishop of New Hampshire in 2003. Dr Jefferts Schori was among the bishops who ratified the election.

So, although the conservative-liberal schism that led to the formation of the Anglican Church in North America (ACNA) took place on her watch, the forces that brought it about were already in play. That did not prevent her becoming a focus of conservative anger.

There followed the steamily disunited Primates' Meeting in Dar es Salaam in 2007, and the slightly more temperate disunity over the meeting in Dublin in 2011 - the meeting was calmer, largely because the Global South Primates boycotted it in protest at Dr Jefferts Schori's attendance.

She declines to be drawn on her relations with the other Primates. Some were warm; others were "civil", she says. "I had conversations with every Primate present at my first Primates' Meeting in 2007. They were not all deep conversations, but most of us will treat each other at least civilly, if not compassionately." Disagreement clearly does not faze her, though her supporters have been irritated over the years by what they see as vacillation within the Anglican hierarchy in its attempts to placate the conservatives.

"There is a long history of disagreement in the Episcopal Church. At heart, it's about how people read scripture. Some people argue for the primacy of scripture, and won't accept that there are other sources of authority.

"It's a very old conflict, and we have always been forming minor splinter groups. We will always find something else to disagree about." She puts conflict into a grand narrative of increasing inclusivity.

"The Episcopal Church has a widening understanding of what it is to be a human, an expanding anthropology, if you will. In the 1700s, a full member of the Church was a white man of majority who owned land; then we considered whether those who did not own land could be members. Next we wondered whether slaves could be members; then we questioned the whole issue of slavery.

"After that, we began to ask whether women could be full members. Then, here in the Episcopal Church, we've looked at the standing of children, baptised but not confirmed. Then gay and lesbian people, then disabled people. . . There will be other groups coming. I don't know who they will be yet. It's a long process of liberation."

She talks of her commitment to the Communion - she calls Anglicans "people of unity, but not of uniformity" - despite the damage, she says, the links have done to her Church's mission. "We are seen as part of a Communion containing those who are hostile to, and pass draconian laws against, gay and lesbian people, [and this] has made it difficult for us in wider society. It's a challenge to us."

Her nine-year term in office comes to an end at the General Convention in Salt Lake City next year. She turned 60 in March this year, and, in the coming months, has to decide whether to stand for another term.

She gives the impression of enjoying the work more as she goes on. "The challenges when I took office were about conflict within the Episcopal Church. Most of that is really behind us, and that has allowed me more time to do ecumenical and interfaith work, and advocacy work."

There remain the expensive property disputes with ACNA congregations, and attendance figures overall continue to decline; but she talks instead about the cultural challenges facing her Church. "Our fastest-growing congregations are international ones, the immigrant and ethnic ones within the US." The challenges are great. "But I don't believe that life is meant to be boring."

Last week, she was awarded an honorary doctorate by Oxford University. More significant, perhaps, given the coolness that Canterbury has shown her in the past, was the message of congratulation sent by Archbishop Welby: "This award, richly deserved, reaffirms Bishop Katharine's remarkable gifts of intellect and compassion, which she has dedicated to the service of Christ. . . It must be noted, too, that Bishop Katharine's achievements serve - and will continue to serve - as a powerful model for women seeking to pursue their vocations in the Church."

END