The conference in Kigali was convened under the auspices of the Global Fellowship of Confessing Anglicans, or GAFCON, a group formed in 2008 that advocates orthodoxy in the global Anglican communion.
The meeting comes two months after the decision of the Church of England to bless civil marriages of same-sex couples.
Clerics from Africa are among those who continue to express concern.
“We are here to bring the Bible to be at the center of everything," Archbishop Laurent Mbanda of Rwanda told the AP Tuesday.
The decision by the Church of England to bless same-sex unions created “enormous confusion” and could be the “final nail in the coffin in the already divided legacy of the Anglican Church," Mbanda said.
The general secretary of GAFCON, Archbishop Ben Kwashi of Nigeria, said in a statement that the Church of England's new stance on civil marriages is “troubling for many Anglicans.”
“We do not seek division, but rather we want to move the mission of God in the world,” the statement said.
GAFCON's chairman, American primate Foley Beach, said during Monday's opening that his group "can no longer recognize" Justin Welby, the archbishop of Canterbury, as the spiritual leader of the Anglican Communion.
“Will you join us in praying for Justin Welby and the bishops he leads?" he said. “You and I must repent and we become Christians again and we follow Jesus Christ.”
Welby has previously acknowledged “deep disagreement” among the provinces, while urging them to try to “walk together.”