The group praised the Episcopalians for making "an official and clear step towards creating a genuinely inclusive church."
Williams faced a similar debate in the Church of England recently.
The Reverend Jeffrey John, who is openly gay, was selected as bishop of Reading in May, but backed out after several Anglican bishops from around the world wrote to oppose his appointment. He said he did not want to damage church unity.
Archbishop of Perth Peter Carnley, the primate of Australia's Anglican Church, acknowledged Robinson's appointment would have a negative impact, but doubted it would tear the denomination apart.
"We have to have a debate about how to apply the biblical principles ... to this modern and contemporary issue," said Carnley, who is considered a liberal voice in Australia's Anglican community.
But conservative Sydney Archbishop Peter Jensen said the new gay bishop would not be welcome in his diocese. He urged Robinson's opponents in the US to fight the appointment by withholding contributions to church coffers.
"For the first time, a branch of our Anglican church has knowingly appointed a person to this senior position who lives in breach of the Bible," he said.
He called the decision "catastrophic," and said it was the beginning of a "loosening of ties" within the Anglican communion.
"Somebody has to break the issue and similar things would have been said about women priests in America 27 years ago," said the Reverend Martyn Percy, a Church of England priest who is director of the Theological Institute at Manchester University in England. He supported the Episcopal Church move.
"I really don't think the argument can be won or lost by appeals to scripture and tradition. The issues are just too complex for that," Percy said. "The Bible is too silent and ambiguous on this."
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