The Most Rev Dr Daniel Deng Bul told reporters at the Lambeth Conference that Bishop Robinson "should resign for the sake of the Church".
"We consider him as a human being. We are not throwing him away. But he is supposed to resign to allow the Church to be united," he said. "The norms of the Anglican Communion have been violated."
He added that those involved with Bishop Robinson's consecration also had to confess.
"We as Christians always forgive one another and confess whenever we make mistakes. If they could do that that would help the Anglican world."
Just under a quarter of bishops in the Anglican Communion have boycotted the Conference in protest of the attendance of pro-gay clergy. The absent bishops, largely conservative church leaders from the Global South, held an alternative summit in Jerusalem last month, the Global Anglican Future Conference (GAFCON).
"I think there is already a breakdown of the Anglican Communion," the Archbishop said. "Three hundred bishops have stayed away from this conference because of Gene Robinson. Shouldn't Gene Robinson resign to allow the 300 bishops to come back to the house?"
The Episcopal Church of the Sudan said in an official statement issued earlier on Tuesday that it could not accept church leaders who practise contrary to the biblical teaching on sexuality.
The Archbishop reaffirmed that position to reporters, saying: "God is not making a mistake creating Adam and Eve. He would have created two Adams if he wanted. But we are saying now God is wrong in creating the different sex. That is a concern."
The Archbishop went on to stress that he and other conservative leaders in the Global South wanted the Anglican Communion to remain united.
"I am here to say let the Anglican world be united. That is my position. I am calling even GAFCON to come back to the Anglican world."
He also warned that the ordination of homosexual clergy and blessing of same-sex couples in the US Episcopal Church had damaged the standing of the Bible and Christians in majority-Muslim countries.
"We are called infidels by the Islamic world...It will give them an upper hand even to kill our people," he said.
The Archbishop of Canterbury, Dr Rowan Williams, said on Monday that he did not believe the Anglican Communion was headed for schism.
"Are we heading for schism? Well let's see. If this is the end of the Anglican Communion, I don't think anyone has told the rest of the people here," he said.
More than 600 bishops have gathered at the University of Kent in Canterbury for the once-in-a-decade Lambeth Conference. The meeting will run until August 3 and cover a range of issues, including social justice, the environment, human sexuality and the draft Anglican Covenant.
