Church leaders say his position is "no longer tenable" after a petition calling for Justin Welby to step down had grown to more than 8,000 signatures last night.
A report last week criticised him for his handling of abuse by the Church of England's most prolific abuser John Smyth QC.
The Bishop of Newcastle, who is a member of the House of Lords, said urgent action was needed over Mr Welby's failure to act on the violent abuse of young men and boys.
Rt Rev Helen-Ann Hartley described the archbishop's position as "untenable" and said he must quit to prevent the Church "losing complete credibility".
She spoke out amid growing concern over the Church's failure to bring barrister Smyth to justice. The "horrific, horrendous and shocking" report said Mr Welby did not follow up rigorously enough on reports of Smyth's "abhorrent" abuse of around 130 boys and men in the 1970s and 1980s.
Mr Welby has admitted that he "failed to ensure" it was investigated when he found out.
Safeguarding
But the archbishop insisted he had "no idea or suspicion of this abuse" before 2013.
Mr Welby knew Smyth because he attended the Iwerne Christian camps in the 1970s, but the review said there was no evidence that he had "maintained any significant contact" with the barrister in later years. The archbishop has so far rejected calls to quit over his handling of the scandal.
But Bishop Hartley said yesterday: "It's very hard to find the words to respond adequately to what the report tells us.
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