"Yes, we will stand with you as long as you remain faithful, biblical, evangelical and orthodox," said Bishop Datuk Yong Ping Chung, who represents South East Asia.
The seven archbishops from Africa, the West Indies, and Asia spoke at the Hope and a Future Conference organized by the Anglican Communion Network.
The network is headed by Pittsburgh's Episcopal Bishop Robert W. Duncan. He helped form the group in 2003 after the Episcopal Church in the United States consecrated an openly gay priest, Gene Robinson, as bishop of New Hampshire and gave tacit approval to blessing services for same-sex couples.
Nigerian Archbishop Peter Akinola said bishops from Duncan's group and others attending the conference must be clear about their allegiance.
"Many of you have one leg in ECUSA and one leg in the network. You must let us know exactly where you stand — are you ECUSA or are you network?" Akinola said, prompting a loud standing ovation.
Although Duncan's group represents a minority of Episcopalians in the 2.3 million-member American church, his group's views are shared by a majority of bishops in the 77 million-member worldwide Anglican Communion, said Douglas LeBlanc, spokesman for Duncan's Anglican Communion Network.
Duncan opened the conference, which runs through Saturday, by drawing a line between the beliefs held by his group and the leaders of the American church.
"These departures are a symptom of a deeper problem, which is the diminution of the authority of Holy Scripture," Duncan said.
Supporters of church policy on gays, meanwhile, have labeled Duncan and his backers as "neo-Puritan" Protestant fundamentalists.
Lionel Deimel, president of Progressive Episcopalians of Pittsburgh, said the archbishops' remarks "could be read as an invitation to leave" the American church.
Deimel called that worrisome but said it was consistent with views he has heard expressed at the conference, among them that the Episcopal Church "has been taken over by a pagan religion" or is "the enemy."
"My preference is that we all stand together and work out our differences and in some cases accept our differences," Deimel said.
But Archbishop Drexel W. Gomez of the West Indies said that's difficult to do because the American church is teaching a "new gospel" that is unclear about God's nature and affirms cultural values, even when they run counter to historic Christianity.
"Anglicanism is really now in a state of flux. ... We are being forced into this by people who are teaching something new and something totally different," Gomez said. "I put the blame squarely on their shoulders."