A vicar facing allegations he reduced Sunday School children to tears after blaspheming at their teacher in front of them has resigned.

Reverend Paul Clarke is accused of using the phrase "Jesus Christ" during a foul-mouthed outburst at the teacher of St Barnabas Anglican church in Mt Eden, Auckland.

Church members say the congregation and Sunday School shrunk after the incident, and about 20 members took their concerns to Auckland Bishop John Paterson.

Vestry members were told of the resignation on Tuesday. He would be offered another position but a formal announcement has yet to be made.

When telephoned Clarke refused to comment. Anglican church spokesman Lloyd Ashton said he was "not at liberty" to comment.

Ashton would not say when an official announcement would be made.

Clarke's wife Ronelle said last week her husband raised his voice after becoming upset at the teacher but could not say for sure whether he blasphemed.

The teacher received a public apology from Clarke through the minutes of the church's annual meeting but has not returned, despite teaching there for 30 years.

Ronelle said last week the allegations were "character assassination" motivated by racism and religious intolerance. She is a South African Catholic of Indian descent, her husband is a former Catholic priest. She accused her husband's critics of telling "utter lies".