Martin said the nuns and Catholic brothers who ran the workhouse-style schools must drop their refusal to renegotiate an intensely criticized 2002 agreement with the Irish government over compensation for victims.
The orders seven years ago agreed to pay euro128 million ($175 million) to the government to be protected from victims' civil lawsuits. In return, the government expects to pay approximately 13,800 victims of physical, sexual and mental abuse and their lawyers more than euro1.1 billion ($1.5 billion).
All those who accept the state settlements, which average euro65,000 ($90,000), must waive their right to sue both the church and government. Their abusers' identities also are kept secret.
Scores of other alleged victims have refused the offer and sued church and state authorities, with mixed results.
The archbishop - whose archdiocese contains more than 1 million of the island's 4 million Catholics - said in an Irish Times column that the church in Ireland has lost credibility because of its weak response to 15 years of revelations of chronic child abuse within its ranks.
Martin said it was incomprehensible why other church leaders remained "in denial" following a nine-year investigation by a child abuse commission, which published its devastating 2,600-page report last Wednesday.
He said the report documented beyond any doubt "church institutions where children were placed in the care of people with practically no morals." The last of those schools for Ireland's poorest children closed more than a decade ago.
The archbishop accused the orders of falling short even on the amount promised to the government. He said the church's failure to complete transfers of cash, property and land worth at least euro128 million over the past seven years "is stunning."
"There may have been legal difficulties, but they are really a poor excuse after so many years," he wrote.
Ireland's most senior leader, Cardinal Sean Brady, later issued a more muted appeal to the orders to give more, saying the 2002 agreement "should be revisited."
The cardinal - who does not have the power to force the orders to pay more - said he and other Irish church leaders expected to meet soon in Rome with Pope Benedict XVI to discuss the scandal. No date has been confirmed.
The Conference of Religious in Ireland, the umbrella body for the church's orders of Catholic brothers and nuns, declined to respond to the comments of Martin and Brady.
Last week the conference, which represents all 18 orders that ran industrial schools, said none intended to make more financial contributions. That provoked fury from victims and some politicians, but not the government.
The government says it has received about euro62 million in cash and church-funded counseling services for abuse victims, while the outstanding euro66 million was to come from the receipt of 64 church properties.
Analysis by independent experts indicates that the offered properties are worth much less today than euro66 million. Ireland's 2008 property market collapse and plunge into recession have slashed values by 25 percent to 50 percent.
Martin said the religious orders must identify "creative ways" to redeem their reputations.
"In many ways, it is your last chance to render honor to charismatic founders and to so many good members of your congregations who feel tarnished," he said.
The Dublin-born Martin, 64, became the church's leader in Dublin in 2004 with a mission to handle the fallout from sex-abuse scandals. Last month he warned Dublin's Catholic faithful they will be shocked and outraged when the next investigation into clerical sex abuse is published this summer.
That Justice Department-commissioned probe seeks to detail how hundreds of priests molested and raped children in Dublin from the 1940s onward while church and state agencies failed to report, punish or stop the abuse.
"It will not be easy reading," Martin wrote. "Let the truth, however, come out."
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On the Net:
Ireland's compensation board for abuse victims, http://www.rirb.ie/
Abuse report, http://www.childabusecommission.ie/rpt/
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