The move by the Global Anglican Future Conference (GAFCON) - which brings together conservative churches mainly from Africa and Asia and claims to represent a majority of the world's Anglicans - highlights a deepening rift within the Church after years of tension over theological and social issues.
"Believing the current instruments of communion no longer meet the needs of the majority of Anglicans around the world, the global Anglican Communion is to be led by a conciliar structure," Bishop Paul Donison, secretary-general of the new council, told the conference in Abuja, Nigeria.
The council will include bishops, priests and lay members, each with voting privileges, GAFCON announced.
It unanimously elected Archbishop Laurent Mbanda of Rwanda as the chairman of the new council but said he would not be "primus inter pares" (first among equals) but rather share power.
Asked if GAFCON members still recognised the leadership of the Archbishop of Canterbury, the group's spokesman Justin Murff said: "The Global Anglican Council recognises Archbishop Laurent Mbanda as its leader."
A spokesperson for the Anglican Communion Office in London said GAFCON's announcement failed to take into account years of consultations over "Anglican identity, structures and leadership".
GAFCON opposes liberal shifts in parts of the Communion, including the ordination of women and greater inclusion of LGBTQ+ members.
The group strongly criticised the Church of England's appointment last October of Sarah Mullally as its first female Archbishop of Canterbury.
She is due to be enthroned as the 106th archbishop of Canterbury on March 25.
The Church of England broke from Rome nearly 500 years ago under King Henry VIII.
Since then, the Archbishop of Canterbury has been the symbolic head of an Anglican Communion that has expanded worldwide through missionary activity, especially in countries that were once part of the British Empire.
Over the last three decades, reforms in the Church of England have allowed women to be ordained first as priests and later as bishops.
But such reforms - along with debate over same-sex relationships - have increasingly pushed the Communion toward what some leaders describe as a breaking point.
Many Anglicans in Africa and Asia, where the Church has been growing fastest, reject the more progressive trends seen in England.
GAFCON, founded in 2008 to counter what members describe as the abandonment of scripture, says it is not seeking to break away from the Anglican Communion but to "reorganise and realign" it around Biblical authority.
One of the proposed reforms aimed at warding off a full schism would dilute the Archbishop of Canterbury's role, creating a rotating international figurehead who would assume some organisational responsibilities while the Archbishop focuses on pastoral duties.
In October, Mbanda said the grouping had "not left the Anglican Communion; we are the Anglican Communion".
While leading prayers on Thursday, he said: "The future has arrived, no turning back".
