LONDON — Sharply divided over issues including same-sex marriage, Anglican leaders from around the world were called on Wednesday to a meeting, planned for next year, that could lead to the transformation of the fractious global church into a much looser grouping.

In a statement, the Most Rev. Justin Welby, archbishop of Canterbury and the spiritual leader of the Anglican Church, invited 37 primates to meet in Britain next January to “discuss key issues face to face, including a review of the structures of the Anglican Communion.”

Among those invited was the leader of the Anglican Church in North America, a conservative alliance that broke away after the decisions by the Episcopal Church in the United States and the Anglican Church of Canada to ordain openly gay people. The Anglican Church in North America is recognized by conservative provinces in the Communion, but regarded by others as an illegitimate splinter group.

After years in which the leadership of the church had sought to persuade those of different views to work together, the convening of the meeting suggests that Archbishop Welby now believes a new strategy is required to confront divisions and prevent the worldwide Communion, in which 38 provinces are formally joined, from splitting apart.