The Episcopal Church consecrated V. Gene Robinson as bishop in ceremony on Sunday despite threats of a permanent schism among the world's 77 million Episcopalians and their fellow Anglicans worldwide as some believe that same-sex relationships violate Christian teaching.
He said his group and most bishops in the international Anglican Communion will not recognise Robinson, who is currently living with his male partner for 15 years, as a fellow bishop.
In an emergency meeting held in London last month, the world's Anglican leaders affirmed their opposition to same-sex relations. Anglican Archbishop of Sydney, Australia, Dr Peter Jensen and senior church leaders in Africa have been at the forefront of opposition to Bishop Robinson's appointment.
Several worshippers also formally voiced their objection to installing an openly gay man as bishop and then walked out of the ceremony held in an ice hockey arena at the University of New Hampshire, which was attended by about 4,000 people, including 50 American bishops.
The head of the global Anglican Church, Archbishop of Canterbury Rowan Williams, said on Saturday the divisions caused by Robinson's consecration were "a matter of deep regret;" however, he believes that any rift would eventually heal.
Robinson told the media that while he doesn't believe his election will lead to a formal split in the 2.3 million-member US church, there could be difficult times ahead but reached out to disgruntled conservatives saying: "They must know if they must leave, they will always be welcomed back."
He has likened the current turmoil to the furore over women, who are not allowed to be priests in a vast majority of Anglican dioceses around the world.
Outside the ceremony, there was heavy police presence on the street; mounted police were also deployed to keep apart Robinson's supporters and protestors.