Members of the General Synod backed a motion on Friday welcoming a joint report published last year, which sets out proposals on how clergy from each church could become eligible to serve in the other.
The report, Mission and Ministry in Covenant, which was co-written by the two churches' faith and order bodies, also sets out how the Methodist Church could come to have bishops in the historic episcopate.
The motion acknowledges that there is further work to do to clarify a number of areas, including how the proposals would be worked out in practice.
It also calls on the Church of England's Faith and Order Commission to update Synod at its next group of sessions in July on this work.
But an amendment to the motion speaks of "confident hope" that outstanding issues can be resolved quickly.
Speaking during the debate the Most Rev Justin Welby, Archbishop of Canterbury said: "I want to support this motion very strongly indeed.
"It seems to me that in voting for it we respond to the word of God in the scriptures where there is a clear command to unity in diversity and in responding to this paper positively we respond to the Spirit who is already working in both of our Churches bringing us together."
After the debate, the Rev Gareth J Powell, Secretary of the Methodist Conference, said: "We are very grateful to the Church of England for this opportunity to address the General Synod and discuss the progress we are making together on the path towards reconciliation and the ordering of our existing ministries in a way that reflects the needs and wishes of both Churches.
"We recognise that these are matters of significance to all within our Churches. As we move forward, we will continue to discern the will of God and deepen our understanding of each other through ongoing dialogue."
Breakdown of votes:
— CofE General Synod (@synod) February 9, 2018
House of Bishops: In favour, 35, against 2, abstentions 0
House of Clergy: In favour 131, against 23, abstentions 13
House of Laity: In favour 124, against 34, abstentions 11
The report builds on the theological merging established by 'An Anglican-Methodist Covenant', signed in 2003, and the following work of the Covenant's Joint Implementation Commission.
In 2014 the General Synod of the Church of England and the Methodist Conference mandated the faith and order bodies to bring forward proposals that would enable ordained church leaders in the two churches to serve in the other.
The Methodist Church said it's unlikely that the proposals will be brought to the Methodist Conference for discussion before 2019.
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