The appointment is opening deep divisions in the Church
Leaders of the Anglican Church in Africa have condemned the appointment of the first openly gay Anglican bishop.
Archbishop Peter Akinola, leader of the Nigerian Church, said the consecration of Gene Robinson meant a "state of impaired communion" now divided the Church worldwide.
"We deplore the act of those bishops who have taken part in the consecration," he said in a statement on behalf of the Primates of the Global South, said to represent over 50 million Anglicans.
The Right Reverend Robinson - who has lived with his male partner for 15 years - was formally made bishop in a colourful but controversial ceremony in the American state of New Hampshire on Sunday.
Irish Primate Archbishop Robin Eames, who heads a commission given the task of preserving the Church's future, said he hoped a looming split could be avoided.
The Archbishop of Canterbury Rowan Williams - the spiritual head of the Church - said the divisions arising in the global Anglican Communion following the consecration were "a matter of deep regret".
Bishop Robinson's appointment would not be accepted throughout the church, he said.
A spokesman for the Ugandan Church, Jackson Turyagyenda, said on Sunday his Church would maintain an earlier position to disassociate itself from the New Hampshire diocese.
One Kenyan bishop, Thomas Kogo, told AFP news agency he would sever all connections with the Anglican Church in the whole of the United States.
"It is unbiblical," he said, "the Bible says we cannot allow such people to work in the Church."
ANGLICAN CHURCH FACTS
70 million baptised members worldwide
38 self-governing Churches
500 dioceses, 30,000 parishes, 64,000 congregations in 164 countries
26 million members in the United Kingdom
17.5 million members in Nigeria
2.5 million members in the US
There has been no official statement as yet from the Kenyan Church.
Elsewhere the bishop of the Australian city of Sydney, Peter Jensen, criticised the appointment, saying his diocese could not recognise Bishop Robinson as fulfilling the criteria laid down in the Bible for a bishop.
Thomas Brown, the bishop of the New Zealand capital Wellington, said he agreed with the Church resolution that homosexual practice was incompatible with scripture, but acknowledged the autonomy of separate parts of the Church.
Archbishop Robin Eames said that while the Church was entering "unknown territory" its leaders had made it crystal clear that they wanted to maintain unity.
"I don't think you can prevent a realignment," he told the BBC, "but I sincerely pray we can prevent ... a split."
He said the Church would aim to minimise the damage as it did following the ordination of women priests in 1992.
"We're still here, because we looked at ways in which the pastoral guidelines could be accepted across the world to maintain the highest possible degree of unity, and I believe we can do it again," he said.
Sunday's 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.
Outside, protesters and supporters of Bishop Robinson were 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.