Leading Commons figures opposed to breaking EU ties without an agreement in place were due to meet on Tuesday, with The Times reporting Most Rev Justin Welby was in talks to chair subsequent citizens' assemblies at Coventry Cathedral next month.
Former Conservative Party leader Iain Duncan Smith told The Times: "I generally don't criticise the archbishop but he shouldn't allow himself to be tempted into what is essentially a very political issue right now."
Britons were exhausted from being told why the result of the Brexit referendum should be overturned, according to Mark Francois, the vice-chairman of the European Research Group of Eurosceptic Tory MPs.
Mr Francois added in the paper: "I suspect they will not be overjoyed by having it rubbed in by the Archbishop of Canterbury to boot."
But the archbishop received support from his fellow clergymen, the Bishop of Buckingham.
The Right Rev Alan Wilson said: "In a mature democracy people would not be afraid of doing this, because it would show what people's concerns and fears and hopes and aspirations around this subject were."
Lambeth Palace has not responded to a request for comment.
Following the 2016 referendum, the archbishop told the House of Lords that the campaign had resulted in an "out-welling of poison and hatred" in Britain.
He added: "It is essential not only in this house but for the leaders of both sides and throughout our society to challenge the attacks, the xenophobia and the racism that seem to have been felt to be acceptable at least for a while."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
