MINNEAPOLIS – The Episcopal Church voted Tuesday to approve the election of their first openly gay bishop, a decision that risks splitting their denomination and shattering ties with their sister churches worldwide.

After a delay caused by an allegation that he inappropriately touched another man and was affiliated with a Web site that had a link to porn, the Episcopal General Convention approved the Rev. V. Gene Robinson as bishop of the Diocese of New Hampshire.

Robinson had been cleared of the accusations a few hours before the vote was taken.

Presiding Bishop Frank Griswold voted 62-45 to to confirm Robinson’s election.

American conservatives and like-minded overseas bishops who represent millions of parishioners have said confirming Robinson would force them to consider breaking away from the church.

The Episcopal Church, with 2.3 million members, is the U.S. branch of the 77-million-member global Anglican Communion, which has been debating the role of gays for decades. A win by Robinson was expected to build momentum for other policy changes that would be favorable to homosexuals.

The Episcopal Church has no official rules — either for or against — ordaining gays.

Some Episcopal parishes already allow homosexual clergy to serve and gays who did not reveal their sexual orientation have served as bishops. But Robinson is the first clergyman in the Anglican Communion to live openly as a gay man before he was elected.

In 1998, Anglican leaders approved a resolution calling gay sex “incompatible with Scripture.” Bishops who hold that view believe that allowing Robinson to serve would be a tacit endorsement of ordaining homosexuals.

Robinson, a 56-year-old divorced father of two, has been living with his male partner for 13 years and serving as an assistant to the current New Hampshire bishop, who is retiring. Parishioners there said they chose Robinson simply because he was the best candidate.

Under church rules, a majority of bishops, clergy and lay people serving as convention delegates had to ratify Robinson’s election.

On Sunday, the House of Deputies, a legislative body comprised of clergy and lay people from dioceses nationwide, approved Robinson by a 2-to-1 margin; a committee endorsed him by secret ballot Friday. The House of Bishops, voted to do the same.

The final vote had been scheduled for Monday but was delayed at the last minute for an investigation of the claims against Robinson.

Bishop Gordon Scruton of Western Massachusetts, who conducted the investigation, determined Tuesday that there was no need for a full-blown inquiry and the debate on Robinson proceeded immediately after.

Scruton said the touching incident “was in public view and was brief” and happened at a church meeting where Robinson put his hand on a man’s back and arm while engaged in a conversation.

The claim of inappropriate touching was e-mailed to Vermont Bishop Thomas Ely by David Lewis of Manchester, Vt. A family friend said Tuesday that Lewis never intended the allegations to go public. Scruton said Lewis told him he did not want to file a formal complaint.

The other concern was a pornographic link found on a Web site of Outright, a secular outreach program for gay and bisexual youth. Robinson helped found the Concord, N.H., chapter of the group, but Scruton said the clergyman ended his association with the organization in 1998 and “was not aware that the organization has a Web site until this convention.”

“In both allegations it is my conclusion that there is no necessity to pursue further investigation,” Scruton said in a speech to bishops.

If conservatives do decide to break away, it is unclear what that would mean for the Episcopal Church. Some parishes could split from their dioceses and refuse to recognize clergy who support homosexuality, but stop short of a complete separation.

A full schism would trigger, among other things, bitter fights over parish assets and undercut the global influence of the U.S. church.

Episcopal Presiding Bishop Frank Griswold and Archbishop of Canterbury Rowan Williams, the leader of the Anglican Communion, each issued pleas for unity before the national meeting began.

Those who support a wider role for gays in the church contend that conservatives exaggerated the potential for a split, and note that among the bishops threatening to leave are some who pledged to walk away before over issues such as ordaining women — then did not follow through.

But many Episcopalians believe the debate over homosexuality has been more divisive.

Bishops from Africa, Asia and Latin America, representing more than a third of Anglican Communion members worldwide, took the unprecedented step this year of severing relations with a diocese that authorizes same-sex blessings — the Diocese of New Westminster, based in Vancouver, British Columbia.

One of the leaders in that split was Archbishop Peter Akinola, head of the Anglican Church of Nigeria, which serves 17.5 million people and ranks second in size to the mother Church of England among 38 Anglican branches.

Some conservative American parishes had already formed breakaway movements, such as the Anglican Mission in America, which remains within the Anglican Communion but rejects the Episcopal Church.

The American Anglican Council, which represents conservative Episcopalians, said before Monday’s vote that if delegates approved Robinson’s election, opponents would hold an “extraordinary meeting” in October to decide their next move.