Two managers of the Vatican bank have resigned after the arrest of a high-ranking cleric with close ties to the financial institution.

Director Paolo Cipriani and deputy-director Massimo Tulli stepped down three days after the arrest of Monsignor Nunzio Scarano.

Msgr Scarano is accused of plotting with two other people to smuggle €20 million into Italy from Switzerland.

Ernst von Freyberg, a German who earlier this year became president of the bank will assume the role of bank director until a permanent replacement is appointed.

The bank has also established a new position of chief risk officer who will be charged with improving compliance with financial regulations at a bank which has long been a byword for secrecy and lack of transparency.

Msgr Scarano, 61, who worked as a senior accountant in the Vatican's financial administration, was arrested along with an Italian secret service agent and a financial intermediary.

According to transcripts from a judge's report, Msgr Scarano, who is under two separate investigations by Italian magistrates in Rome and Milan, mentioned the director in phone conversations tapped by police investigators.

The judge's report says Msgr Scarano controlled vast amounts of money and felt he could act with impunity because of his connections to the Vatican bank.

Two days before the arrests, Pope Francis set up a commission of inquiry into the Vatican bank, which has been hit by a number of scandals in the past decades.

Msgr Scarano was for years a senior accountant for a Vatican department known as APSA, whose official title is the Administration of the Patrimony of the Apostolic See.

The case against Msgr Scarano came as an embarrassment to Pope Francis, who, since his election in March, has pointedly eschewed many of the trappings of office and sought to stress the importance of a simple life of devotion.

The bank, officially known as the Institute for Works of Religion, tarnished by accusations of failing to meet international transparency standards intended to combat money laundering and tax evasion, is trying to clean up its image after a long history of scandals.

The European anti-money laundering committee, Moneyval, said in a July report that the IOR still had to enact more reforms in order to meet international standards against money laundering.