Under previous practice, people caught illegally crossing the border were returned to Mexico after a guilty plea and a brief detention. The violation is a misdemeanor under federal law.
Sessions said the Department of Justice would take up as many referrals from DHS "as humanly possible."
However, Feasley warned that there are many dangers of family separation. It is "extremely traumatic" for children to experience, especially after a lengthy, stressful trip to the U.S. Very young children have been separated and left with strangers, many of whom do not speak their language.
"Then these children are put into shelter facilities which are confined spaces. The experience is doubly traumatizing," Feasley continued. "The American Academy of Pediatrics has cautioned against the long lasting emotional trauma and harm that separation can cause children."
Some migrants have tried to challenge their treatment under U.S. authorities.
One Honduran woman, Olga George, was charged with illegal entry and separated from the four young children accompanying her. She has retained lawyers who charge that the Justice Department is discriminating against her for being a Central American.
A Congolese woman who sought asylum was detained and separated from her young daughter for months until DNA testing during court proceedings confirmed their identities.
If immigrants detained at the border have valid asylum claims, they could still receive federal criminal convictions on their record regardless if they are judged to have a right to stay in the U.S., CNN reports. However, there are no special arrangements under the current plan for those who claim asylum when they are detained.
Department of Homeland Security secretary Kirstjen Nielsen officially enacted a "zero-tolerance" policy on Friday May 3.
Nelsen has said that families are separated only for the children's safety or when family relationships can't be proven. Under federal law and court decisions, children must be released from detention quickly. Previously, this meant entire families were released rather than separated.
DHS has already referred over 30,000 illegal entry cases to the Department of Justice, an increase of 61 percent over Fiscal Year 2017.
(Story continues below)
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Feasley said the new policy will not address "the pervasive root causes of migration." Migrants are fleeing state- or community-sanctioned violence, poverty, lack of educational opportunity, forced recruitment into gangs, and domestic abuse, among other grave problems that compel children and families "to take the enormous risks of migration."
"These are the factors that must be addressed as we look to repair our broken immigration system," she said.
Feasley also had particular recommendations for Catholics.
"Catholics should try to remember the human dignity of all families and children who arrive and look to assist these families in productive ways that help them comply with our immigration laws--ensuring that they know their rights and responsibilities in this country," she said. She suggested helping migrants get legal counsel, accompanying them to legal proceedings, and "welcoming and praying with and for these families in our parishes."
"As Pope Francis says, they are not a problem or a burden but an opportunity for encounter," she told CNA.