A Vatican-appointed bishop will fly into Scotland next week to investigate allegations of sexual misconduct surrounding Cardinal Keith O'Brien, it has emerged.

O'Brien's successor as archbishop of St Andrews and Edinburgh, Leo Cushley, announced the unusual step in letters sent to his clergy this week, according to the National Catholic Reporter (NCR).

The Pope's spokesman, Federico Lombardi, told the Guardian he had "nothing to add" to the report, which said that, following a request from Pope Francis, the Maltese auxiliary bishop Charles Scicluna would visit the archdiocese from 8-10 April.

According to the NCR, Cushley's two letters said Scicluna, the Vatican's former sex crimes prosecutor, would "listen to and report the testimony offered by past and present members of the clergy … concerning any incidents of sexual misconduct committed against them by other members of the clergy whomsoever."

The bishop – who co-represented the Holy See at a fierce public grilling by a United Nations panel of experts in January – has asked those wishing to speak to him to "prepare their narrative in writing", Cushley reportedly added. The letters reportedly do not mention O'Brien by name.

The move comes more than a year after O'Brien resigned amid allegations published in the Observer of sexual misconduct from three priests and one former priest. The Vatican subsequently ordered him to spend a period of time in "prayer and penance".

Last month, one of the men appealed directly to Pope Francis to intervene, describing the church as a "formidable machine" and accusing officials of having "passed the buck, misrepresented the truth, engaged in cover-up and … shamelessly procrastinated".

"I want to ask Pope Francis can you sort this out?" the man told the Observer.

As the Argentinian pontiff marked his first year on the papal throne last month, his response to the sexual abuse scandal was singled out by many observers as a blind spot in an otherwise impressive record.

In a statement, Cushley reportedly said Scicluna's visit was "a positive step towards truth and eventual reconciliation". "This may not be an easy thing to do, but it is the right thing to do," he added.

A spokesman for the archdiocese did not return requests for comment.