The service was held at St Bartholomew the Great Church
The Church of England's two most senior figures have expressed concern after the "marriage" of two gay priests was held at a London church.
The Archbishop of Canterbury, Dr Rowan Williams, and the Archbishop of York, Dr John Sentamu, said an investigation was taking place into the service.
The couple - the Reverend Peter Cowell and the Reverend Dr David Lord - were already civil partners.
But the vicar who performed the ceremony insisted he had no regrets.
Writing for the New Statesman website, the Reverend Dr Martin Dudley said refusing to bless the pair "would have been a negation of everything I believe".
Critics say the service, held in May at St Bartholomew the Great Church in the City of London, broke Church guidelines.
In a statement, the Archbishops expressed "great concern" over reports of the service.
Those clergy who disagree with the Church's teaching are at liberty to seek to persuade others
They said they could not comment on the specific circumstances of the case because a an investigation had been launched by the Bishop of London.
But they said "various reference points" to the Church of England's teaching on sexuality were "well known" and remained in place.
"Those clergy who disagree with the Church's teaching are at liberty to seek to persuade others within the Church of the reasons why they believe, in the light of Scripture, tradition and reason that it should be changed," they added.
"But they are not at liberty simply to disregard it."
But Dr Dudley, who insisted he was "robustly heterosexual", wrote that he had not carried out the ceremony to provoke traditionalists.
The Reverend Martin Dudley, who performed the service, said he had no regrets
"It is not we who have whipped up the whirlwind, replacing words of love and inclusion with those of hatred and exclusion," he added.
He described the service as "not a gay rally or demonstration, but a truly joyful celebration".
"Amazing flowers, fabulous music, a ceremony both solemn and oddly homely, familiar words reordered and reconfigured, carrying new meanings.
"Nothing jarred, nothing felt even vaguely inappropriate. New and untried - but not wrong."
The couple are said to have exchanged vows and rings in front of hundreds of guests in the event, thought to be the first of its kind in the Anglican Church.
Anglicans worldwide are split over homosexuality and conservatives have condemned the service - which had no legal status - as blasphemous.
Critics say the wording of a traditional wedding expressly defines marriage as being between a man and a woman.
But liberals in the Church say the Bible should be reinterpreted in line with contemporary experience.
Under Church of England guidance, gay priests can enter civil partnerships as long as they remain celibate.
Guidance also says that gay couples who ask a priest to bless their partnership must be treated "pastorally and sensitively".
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