The appointment is opening deep divisions in the Church
Members of the Anglican Church across the world are debating its future after the consecration of its first openly gay bishop.
Gene Robinson - who has lived with his male partner for 15 years - was formally made bishop of the US state of New Hampshire in a colourful but controversial ceremony on Sunday.
Three church members were given the opportunity to voice their objections during the ceremony and one woman said the consecration would not only rupture the Anglican community but "break God's heart".
Within minutes of the service ending, the Archbishop of Canterbury Rowan Williams - spiritual head of the Anglican Church - said the divisions arising in the global Anglican Communion following the consecration were "a matter of deep regret".
But the archbishop's carefully worded statement avoided direct criticism or endorsement of the consecration which he said had been made "in good faith".
"The effects of this upon the ministry and witness of the overwhelming majority of Anglicans particularly in the
non-western world have to be confronted with honesty," he added.
Some of the bishop's opponents say they plan to set up a new church structure with like-minded bishops from the US and abroad.
The BBC's Susannah Price, in New Hampshire, says his supporters are hoping to avoid a permanent split, but it is too early to tell what the long-term effects of Sunday's consecration will be.
The consecration service, at a specially converted ice-hockey arena in the town of Durham, was held amid tight security, with police on rooftops and in heavy presence on the street.
About 4,000 people, including 50 American bishops, as well as Bishop Robinson's family and parishioners, attended the ceremony.
There was an impassioned standing ovation in the arena before he was presented with brightly coloured vestments by members of his family, including his mother and father.
And then, his voice cracked with emotion, he spoke, saying "You cannot imagine what an honour it is for you to have called me."
He reached out to disgruntled conservatives, saying: "They
must know if they must leave, they will always be welcomed
'Symbol of unity'
Earlier, when Presiding Bishop Frank Griswold asked the congregation: "If any of you know any reason why we should not proceed, let it be made known," three church members made speeches.
But the consecration sermon by New Hampshire's retiring Bishop Douglas Theuner was interrupted twice by vigorous applause as he defended Robinson.
Bishop Robinson "will stand as a symbol of the unity of the church in a way none of the rest of us can", he said
Outside, protesters and supporters of Canon Robinson faced each other off, kept apart by mounted police, while a separate service for those against the consecration took place in a church in another part of the town.
Some traditionalists, who view homosexuality as a violation of the teachings of the Bible, plan to ask the spiritual leader of the world's Anglican Christians, Archbishop of Canterbury Dr Rowan Williams, for permission to split from the Church.
But, despite the deep divisions, Dr Williams has predicted the rift will eventually heal.
"God will still teach us in our separateness; and one day we shall be led, in both thankfulness and repentance, to share with one another what we have learned apart," he said before the ceremony.
Senior church leaders in Africa have been at the forefront of opposition to Bishop Robinson's appointment
Archbishop Peter Aioli, the primate of the Nigerian Church, the largest in the Anglican community, called the bishop's sexuality an abomination.
Reverend Peter Karanje, provost of All Saints Cathedral in Nairobi, said he was deeply saddened to hear of the appointment, but he said church leaders in Kenya still hoped some way could be found to avert a split in the communion.
Speaking before his consecration, Gene Robinson told the BBC he felt calm and at peace and he was not concerned that he will not be widely accepted as a bishop abroad.
"Well, it makes me feel like I'm in very good company because most of the bishops around the world wouldn't recognise the ministries or ordinations of our women priests and our women bishops.
"The other fact is that I'm not welcome now as an openly gay priest in most of those places," he said.