Dr Murray stepped aside over his "inexcusable" failings when investigating complaints against notorious paedophile priest Fr Thomas Naughton when he too was an auxiliary bishop in Dublin.
This dramatic second resignation will intensify pressure on two existing Dublin auxiliaries, Eamonn Walsh and Ray Field, to quit as well even though both have told Archbishop Diarmuid Martin that they did no wrong and that it would be a miscarriage of justice for them to resign or be fired.
He has also strongly criticised Archbishop Martin's impassioned plea for him to accept collective responsibility for the cover-ups as questioning his personal integrity.
A sixth former Dublin auxiliary, Dermot O'Mahony, who is in retirement, resigned from the presidency of a body which organises annual trips to Lourdes for the disabled and has been ordered by Archbishop Martin not to administer Confirmation to children next spring.
Last night four informed sources in Dublin and Kildare separately said that "Bishop Moriarty will resign tomorrow in order to give his diocese a fresh start for 2010".
One source suggested that over the weekend Bishop Moriarty (73) decided after intense consultations with trusted colleagues and friends at his residence in Carlow that he would go quickly.
An announcement of acceptance of his resignation by Pope Benedict could come as early as midday today, Rome time.
Other sources, however, questioned this timescale and suggested that Bishop Moriarty plans to say today that he has offered his resignation to the Holy Father.
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