The Church of England's bishops appear to be at war with themselves after some distanced themselves from a statement reiterating longstanding Christian teaching that sex is for male-female marriage only.

The Bishop of Gloucester, Rachel Treweek, said that she was "deeply frustrated and saddened" by the way the statement was published. She continued: "I recognise that it has fanned into flame unnecessary pain and distress and I wish to acknowledge my part in that."

In their document, published in response to the introduction of mixed-sex civil partnerships, the House of Bishops said last week: "For Christians, marriage – that is the lifelong union between a man and a woman, contracted with the making of vows – remains the proper context for sexual activity."

It added: "Sexual relationships outside heterosexual marriage are regarded as falling short of God's purposes for human beings. The introduction of same sex marriage... has not changed the church's teaching on marriage or same sex relationships."

But Bishop Treweek said: "The word 'love' emanating from the generous love of God is one that needs to be heard and lived and I am extremely sorry that it has not been heard in the publication of the House of Bishops statement."

She was supported by the Bishop of Sheffield, Pete Wilcox, who on Twitter described her statement as "very helpful comment". The Bishop of Gloucester's statement was also retweeted by the Bishop of Manchester, David Walker, and the Bishop of Edmonton, Rob Wickham.

The Bishop of Liverpool, Paul Bayes, retweeted a statement from gay campaigner Jayne Ozanne which described the House of Bishops' document as making the Church of England "a laughing-stock".

Leading evangelical and social commentator Rev Peter Ould responded on Twitter to Bishop Treweek's statement by declaring that those who were upset by the House of Bishops' statement – including bishops themselves – were guilty of "faux perplexity" and "emotional immaturity" since they must themselves understand how the Church of England works and therefore could not have been surprised or perplexed by its publication.

He added: "What perplexes me, though, is Bishops who renege on their ordination vows and teach contrary to the doctrine they took vows to uphold."

The president of Gafcon UK, Bishop Michael Nazir-Ali, welcomed the House of Bishops statement, declaring: "The clear stating of the Church's biblical and historic teaching on the nature of marriage – that marriage between one man and one woman is the proper context for sexual expression and that sexual relationships outside such an understanding of marriage fall short of God's purposes – is very much to be welcomed by all Bible-believing and orthodox Christians."

But he said that although "the Bishops' Statement is clear about the Church's understanding of marriage and the relationship of sexual expression to it, it is less clear about the consequences of such an understanding for clergy and their ordination vows, and what should be required of lay people so that they too may order theirs and their families' lives in ways that are consistent with the teaching of the Bible and of the Church."

He added: "It is my prayer that the Bishops will go on to provide such clear guidance which cannot be misunderstood in matters having to do with our salvation."

The Church of England is due to complete later this year a lengthy process called 'Living in Love and Faith' (LLF), which is examining contemporary moral issues. It has already been made clear this will "not pronounce on the rights or wrongs of same-sex marriage" – thus by implication leaving existing Church teaching in place – but "helping people to learn how to think," according to, Bishop Christopher Cocksworth, chair of its co-ordinating group.

Bishop Cocksworth added that the LLF project was driven by the fact that people are "in need of wisdom to order their loving and sexing well", the Church Times reported. 

David Baker is a former daily newspaper journalist now working as an Anglican minister in Sussex, England. Find him on Twitter @Baker_David_A