After the theft of a set of 100-year-old figurines of the 12 Apostles, Mr McConachie surprised his congregation at St Dunstan's, in West Peckham, near Maidstone, Kent, last week by reciting St Mark, Chapter 9, Verse 43: "And if thy hand offend thee, cut it off.
"It is better for thee to enter into life maimed than having two hands to go into Hell, into the fire that never shall be quenched."
The Londonderry-born vicar suggested that a state-appointed body should be created to perform the amputations, and proposed that only one hand be chopped off initially, to see if it achieved the desired effect.
The Bishop of Rochester, Michael Nazir-Ali, has sent a message to Mr McConachie, 56, summoning him to a private meeting and making clear that he does not share his interpretation of the New Testament.
He told him, according to a spokesman for the diocese: "Jesus's teaching has nothing to do with punishment to be inflicted on others. In fact, any adequate view of punishment must, for Christians, include the possibility of reform and rehabilitation.
"This excludes the mutilation of the body, as it would make rehabilitation more difficult."
After his blast from the pulpit, Mr McConachie acknowledged that he was following the Scriptures very literally, but declared that cutting off the thieves' hands would make them think twice before doing it again.
The diocesan spokesman said: "The meeting will be a private matter. Bishop Michael is very concerned for his diocese, of which St Dunstan's Church is part."
The figurines have now been returned to the church, after being tracked down to an antiques dealer in north London.