Orange Order, Royal Black Institution and Independent Orange Order representatives have held talks with Catholic Primate Dr Seán Brady.
The loyal orders said the talks were part of their mission to explain their belief that the Parades Commission should be replaced by a more equitable system for regulating marches.
A spokesman described the meeting with Archbishop Brady as "a cordial, businesslike and useful exchange of views held in an atmosphere of concern for the coming months which all sides wish to see pass in an entirely peaceful manner".
The loyal orders said they believed the Parades Commission, formed in 1997 to rule on contentious parades, had failed and should be replaced.
"We recognise that there has to be regulation but presently this is focused on parades organised by the loyal orders - and that, we believe, is biased and unfair. The Parades Commission has, furthermore, shown itself to be a failed and increasingly farcical body that must be replaced with a more equitable arrangement that will seek to develop the widest possible consensus from within the community," they said.
The discussions in Armagh are the latest in a series of meetings initiated by the loyal orders.
They have already held talks with Northern Secretary Peter Hain, Northern Ireland Office Minister Paul Goggins, Minister for Foreign Affairs Dermot Ahern, the Northern Ireland Human Rights Commission as well as the political parties and other churches.
The controversial Whiterock parade is scheduled to take place in north Belfast later this month, shortly before Taoiseach Bertie Ahern and prime minister Tony Blair arrive for talks aimed at restoring devolution.
The annual Drumcree parade will take place in early July before the culmination of the summer marching season on July 12th.