Michael Fabricant said that following an intervention by the Archbishop of Canterbury the Church of England should "seize the opportunity" to allow same-sex weddings.
The Archbishop, Justin Welby, who is leader of the global Anglican church, risked the ire of conservative bishops after pledging not to discipline churches that allow gay couples to wed.
And Mr Fabricant called on churches to "do God’s work" by holding marriages for gay couples. He said: "I hope that Lichfield Cathedral might lead the way on this.
"There are many Christian congregants in same-sex relationships whose joy would be fulfilled by marriage in Lichfield’s beautiful 13th Century cathedral.
"I realise I will anger the intolerant by expressing these views, and I have no authority over the Church of England in any event.
"Still, I hope my comments will cause some reflection and that maybe some priests will seize the opportunity that the Archbishop has presented."
The Most Revd Welby addressed the issue in a speech to more than 650 bishops at a once-in-a-decade gathering of the Anglican Communion.
He said: "I neither have, nor do I seek, the authority to discipline or exclude a church of the Anglican Communion. I will not do so."
However, he also confirmed the validity of the 1998 Lambeth 1.10 declaration, which states that marriage is "between a man and a woman" and that same-sex relationships are not in accordance with the Bible.
Mr Fabricant said the Archbishop had made a "clever compromise" and suggested the church should be split into two camps.
"Some bishops from the Anglican communion community, particularly those from Africa, south Asia and other developing countries, do not exhibit the same tolerance and love for all their congregants that we do in the West," he said.
"This has already caused schisms particularly in some Anglican churches in the United States.
"I do sometimes wonder whether on balance the Anglican community would be better splitting into two different communions; the tolerant and the intolerant, with the Archbishop presiding over the tolerant wing."
Anglican churches in countries including Scotland, Wales, the USA, Brazil and Mexico either conduct or bless same-sex marriages.