The Evangelical Alliance has issued a comprehensive rebuttal of accusations made against it by the Barnabas Fund and Barnabas Aid International charities in a booklet entitled Hard Pressed On Every Side.

The Barnabas booklet, sent to thousands of supporters and made available online, alleged the charity was ignored in favour of other religious liberty organisations and that its former General Secretary, Rev Joel Edwards, had "urged churches to open their pulpits on Sundays for Muslim preachers".

It says the EA urged the World Evangelical Alliance to "break its partnership with Barnabas Fund" and that the Barnabas trustees "are very sad to see how the EA UK's current leadership is moving away from conservative evangelical values".

When the booklet was released in February the EA said it was "surprised and saddened" by the comments made in Hard Pressed on Every Side and was "dismayed that the trustees chose not to discuss their allegations with us first to avoid misinformation and confusion".

It said: "We have written to both organisations seeking to clarify who has issued this document and with what authority and asking for evidence for comments which appear unfounded."

Two meetings between Barnabas and EA representatives followed, which the EA said were held in a "warm, gracious and business-like manner". At the second of these meetings the Barnabas representatives were shown the EA response and invited to comment.

The EA said it was "with sadness" that it had made the document public. However, it continued, the nature of the Barnabas booklet, its wide circulation and the "questions and confusion that have resulted among our members and others" left it "needing to make what we trust will be regarded as a carefully-measured response".

The EA denies it marginalised Barnabas before the charity's resignation in 2013 and points out that its founder Patrick Sookhdeo – currently facing a charge of indecent assault which is due to be heard next February – wrote a major article for its Idea magazine. It says Barnabas Fund has provided no evidence to support its claims.

The EA flatly denies the Barnabas claim that its former general director Joel Edwards had "urged churches to open their pulpits on Sundays for Muslim preachers". It cites a sentence from an article in 2006 in which Edwards said: "Imagine the impact if every Christian community invited a Muslim cleric to its worship service to explain his faith and how they viewed Christianity." The EA says Barnabas' account "seems an unfair representation on either Joel's content or indeed his motivation", adding: "Had this been a matter of concern to BF leadership, we would have hoped they would have raised this matter during the seven years before their resignation from EA, or indeed, in their letter of resignation."

The EA says it declined advertising from Barnabas because of the charges against and later conviction of Sookhdeo on a previous sexual assault case and informed the World Evangelical Alliance of the situation as it was exposed to "reputational risk" if it continued to associate with the charity.

It denies the Barnabas accusation that was "moving away from conservative evangelical values", saying: "The leadership of EA has worked hard to maintain and develop good relationships across the full breadth of evangelicalism. Our commitment to evangelism, biblical literacy, religious liberty, an orthodox, biblical approach to human sexuality and a biblical view of marriage, has reinforced our historic evangelical values."

Hard Pressed On Every Side criticised a number of individuals and Christian organisations. Among them was this website, which revealed details of Sookhdeo's treatment of former trustees and the failure of Barnabas Aid International to accept he was guilty of indecent assault and intimidating witnesses.

The booklet also criticised the Church of England, which it accused of racism towards Sookhdeo, Open Doors, Release International and Christian Solidarity Worldwide. It accused Muslims in Colorado Springs of manipulating search engine results to improve the ranking for articles "biased against" Sookhdeo. It also claims his car was "apparently deliberately sabotaged" in a "life-threatening incident".

The booklet also refers to a meeting of 12 senior Anglican leaders in April 2015 at the London offices of Christian Concern which concluded that he had been "deliberately targeted" and was innocent of the charges of sexual assault and intimidating witnesses. It claims that a "representative of the Archbishop of Canterbury was present". However, a spokesman for the archbishop told Christian Today: "A Lambeth Palace staff member attended the meeting as an observer only and was not representing the Archbishop of Canterbury. The staff member did not have a decision-making role and any decisions made during that meeting were a matter for the Barnabas Fund."

Barnabas Fund has been asked to comment on this story.