In the script of a homily to be delivered at the Festival of Peoples in the Pro Cathedral in Dublin this evening, Dr Martin said many Irish people were "quietly opting out of integration by sending their children to schools with low levels of diversity".
The archbishop said he was proud of the record of Catholic schools in integrating children of new communities, but called for an "open and honest debate" on the future of the school system, one which he said should not just be about "point scoring".
He said rent policies and inadequate planning could also lead to an unhealthy environment which even the best schools would not be able to address. He said he was committed to working with others to address challenges.
"I sometimes feel that some of the pundits who comment on the role of Catholic schools in the process of integration have not seen for themselves the success story of integration that I see in so many parts of this diocese. We need open debate on the future of our educational system, but we need honest debate," he said.
Dr Martin said integration is a task and challenge for all in Irish society. He urged immigrants coming to Ireland in search of a better life to be proud to be in Ireland, be proud to the Irish but not to "lose the richness of the traditions they bring here".
"Ireland is big enough to embrace you. Respect the country that welcomes you and that Irish society welcomes you," he said.
In his homily, Dr Martin said Pope Benedict's words on the danger of modern society becoming just an "aggregation of neighbours" ring true also in Dublin.
"I am struck at the change in Dublin society where we find areas which once affronted the difficulties of life with a true spirit of caring, community and solidarity, now turning into walled citadels where consumerist anonymity prevails," he said.
"Relationships too can also become caught up in walls; in the walls of intolerance, of feelings of superiority, in latent or even express racism.
"The social, economic and political future of Ireland, with the particular challenges that the coming years will bring, will require that we all work together to build a society not just of anonymous next-door neighbours but of people of varied backgrounds committed to building new community," Dr Martin added.
The Festival of Peoples, initiated by Archbishop Martin in 2005, is a liturgical celebration of the new multicultural society in Dublin.
People representing new communities, many in native dress will take part in the liturgy, which will incorporate a number of languages and music from different nations.
Among those taking part in the event at the Pro Cathedral at 6.30pm will be representatives of the Polish, Filipino, Lithuanian, Nigerian, Romanian, Indian, Croatian, Czech and Palestinian communities.
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