The Catholic church should contribute substantially and willingly to the cost of righting wrongs surrounding a mass grave at one of its former homes in Ireland, the Government said.
Pope Francis vowed to pursue justice for victims of church abuse during his two-day trip to the country and has pledged to study an official memo about a property in Tuam in Co Galway.
Between 1925 and 1961 around 800 infants were buried in a septic tank at the home for unmarried mothers and their children.
It was a "shameful" chapter in Irish history and the church must take real action, quickly and unconditionally, to make reparation to those who lived at the residence, Irish Children's Minister Katherine Zappone wrote in a letter to the pontiff.
She added: "It is my strong conviction that given the role of the church in this shameful chapter of recent Irish history it must play a practical role in addressing the hurt and damage."
The minister raised the issue with the pontiff on Saturday.
She wrote: "I believe that the church should contribute substantially to the cost of whatever option is decided by the government.
"This should be done willingly, unconditionally and quickly.
"Nothing less will demonstrate remorse."
Francis ended his historic visit to the country by seeking forgiveness for a dark litany of clerical crimes.
Addressing a large crowd of pilgrims at an open air Mass in Dublin's Phoenix Park on Sunday, he laid bare the many forms of abuse and mistreatment meted out to children and vulnerable adults in past decades.
The attendance figure was significantly down on more than a million who greeted his predecessor Pope John Paul II when he said Mass at the same spot 39 years ago. It also appeared to be well below what organisers predicted before this weekend.
Bad weather, long walks for pilgrims and a campaign by protesters to obtain tickets then not show up may have contributed.
The legacy of church abuse cast a long shadow over the first papal visit to Ireland since 1979, as the pontiff repeatedly moved to address the scandals and said he viewed those who covered up clerical child abuse as "filth".
His words drew praise in some quarters, the leader of the Catholic Church in Ireland said he was moved and shocked by what survivors told him, but others accused him of not going far enough.
On Monday, victims called on the pontiff to deliver a plan of action.
Mark Vincent Healy from Dublin said: "This Pope has actually done nothing."
Meanwhile, the Catholic Archdiocese of Dublin disclosed a positive spin-off from visit.
The car used by Pope Francis during his trip to Ireland is to be donated to help homeless families.
It will be given to the social care agency of the Catholic church in Dublin, Crosscare.