The SDLP leader, Mr John Hume, has called on everybody in Northern Ireland to work together for a better economic future as a way to "break down the bitter barriers of the past".
In his New Year's statement, Mr Hume said that improving people's social and economic conditions would automatically lead to a healing process in society.
"We are entering a new century and a new millennium, so let us make it a new real beginning for all of our people. The means for doing so are already there, since our new institutions are in place and our representatives from all sections of our people are working together on our common ground.
"Our common ground is our social and economic future and the more we succeed in developing that ground the more we will break down the bitter barriers of the past and the healing process will be very clear."
Celebrating Mass yesterday in St Patrick's Church, Belfast, the Bishop of Down and Connor, Dr Patrick Walsh, stressed the need for dialogue between the North's different traditions.
"We must learn to recognise and cherish and respect cultures other than our own and to appreciate the richness of diversity. This can only be achieved by dialogue between cultures and such dialogue must be based upon the mutual recognition that there are values which are common to all cultures because they are rooted in the nature of the human person," Dr Walsh concluded.
In his New Year's statement, Dr Philip Weir, chairman of the Ulster Young Unionist Council - an Ulster Unionist group highly critical of the Belfast Agreement - said peace had to be accompanied by truth and justice.
"Morality cannot be allowed to become a roadside casualty in a tunnel-vision charge for peace. Public representatives must be willing to acknowledge the dreadful errors of the past. The delineation between right and wrong cannot be muddied. The children of Northern Ireland must know of the mistakes of the past in order to learn from them," he concluded.