The event is seen as a rival gathering to the Lambeth Conference which Justin Welby will host next year.
While all Anglican bishops have been invited to the Lambeth Conference on 27th July - 1st August 2020, some have suggested they won't attend in protest at what they perceive as a move towards a more liberal position on sexuality within the Anglican Communion.
In a statement announcing the GAFCON event, leaders said: "On the one hand, we have no interest in attempting to rival Lambeth 2020. On the other hand, we do not want our bishops to be deprived of faithful fellowship while we wait for order in the Communion to be restored.
"Therefore, we have decided to call together a meeting of bishops of the Anglican Communion in June of 2020. The conference will be primarily designed for those who will not be attending Lambeth, but all bishops of the Anglican Communion who subscribe to the Jerusalem Declaration and Lambeth Resolution I.10 are invited to join in this time of teaching, worship, and fellowship."
In a question to Dame Caroline Spelman, who represents the Church in Parliament, Tory MP Sir John Hayes asked whether Justin Welby plans to join the meeting in Rwanda.
In her response, she said: "At previous meetings of the Global Anglican Future Conference the Archbishop of Canterbury has been represented by a diocesan bishop of the Church of England.
"No decision has yet been taken by the Archbishop of Canterbury about whether he or a representative will attend the 2020 Conference in Kigali."
Around a thousand bishops are expected to gather for the Lambeth Conference next year - its unknown how many will attend the GAFCON event.
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