Cardinal Keith O'Brien has been accused of inappropriate behaviour by four priests.
The most senior Roman Catholic cleric in Britain will have a say in the election of the successor to Pope Benedict XVI.
A statement read out in St Mary's Cathedral, Edinburgh - where Cardinal O'Brien had been due to take Mass - said the Church leader contested the claims and was seeking legal advice.
The accusations against the Cardinal, reported in the Observer, go back 33 years.
The four priests have made complaints to nuncio Antonio Mennini, the Vatican's Ambassador to Britain, and are demanding his immediate resignation.
According to the Observer, one priest accused the Cardinal of making an inappropriate approach in 1980, after night prayers at St Andrew's College, Drygrange, where he was a seminarian.
A second complainant says there was inappropriate contact with the cardinal during a visit from him in his parish.
Another priest claims he was faced with "unwanted behaviour" by the Cardinal after a late night drinking session.
A fourth complainant also claims inappropriate behaviour by the Cardinal after night prayers.