Dr Martin met with the Association of Catholic Priests in Ireland (ACP) in a 'gloves-off' meeting, in which he was told the Diocese of Killala was near breaking point with just four priests under 50.
At the meeting in Dublin, ACP spokesman Fr Brendan Hoban accused Rome of not appreciating the seriousness of the situation.
The archbishop is the most senior Irish prelate to hold talks with the group to date.
The ACP told Dr Martin that solutions such as the clustering of parishes and bringing in priests from abroad were "not realistic" and the church needed to think "outside the box".
They also discussed rebel priest Fr Tony Flannery. Dr Martin was told the procedures for dealing with "allegations of unorthodoxy against priests" were perceived to be "seriously defective and unjust".