In at least 126 cases, the authorities said, babies born to unmarried mothers were adopted and their adoptive parents’ names were written on their birth certificates, instead of the name of the birth mother.

Mr. Finlay said the St. Patrick’s Guild was one of at least seven large adoption agencies that operated in Ireland then. It was a time when unwanted pregnancy carried so much social stigma that many young women and their parents went to great lengths to conceal it.

Many smaller institutions were also involved in arranging adoptions, with little or no supervision. As they closed, their files were handed over to the government’s child protection agency, Tusla.

Tusla took over the St Patrick’s Guild files in 2016 and discovered, while attempting to help adopted children trace their birth parents, that some of the births had been fraudulently registered. In a statement, it said it had referred the fraudulent registrations to the police. But few if any of the people responsible are likely to be still alive.

Officials at the child protection agency said their main priority now was to identify and locate all the people whose birth certificates were falsified.

“We are very aware that this will be a shock for people affected and may cause upset and anxiety,” the agency said in its statement. “We will work closely with people throughout and offer support, including counseling, while allowing them their autonomy to decide what steps they want to take.”

Wednesday was not the first time Irish officials felt obliged to apologize for the treatment of unwed mothers. The government has also apologized for the conditions at church-run homes for mothers and babies, and at Magdalene Laundries, where women were forced to work.