Both St. Andrew’s Catholic Church in Sag Harbor and St. Rosalie’s Catholic Church in Hampton Bays are named in civil lawsuits filed last week, charging that priests assigned to those parishes molested children under their care during the 1970s.

The lawsuits were among hundreds filed across New York State against the Catholic Church, the Boy Scouts of America and other institutions starting on August 14, when the statute of limitations, which would ordinarily bar many of the lawsuits from being filed, was suspended for one year.

The one-year window was adopted earlier this year when the State Legislature amended the Child Victims Act. The law originally required a suit to be filed before the child victim had reached the age of 23. The statute of limitations has now been extended to the age of 28 for a victim to seek felony criminal charges, or 25 for a victim to press misdemeanor criminal charges. The statute of limitations for civil lawsuits has been extended to age 55.

Jennifer Freeman, an attorney with the Marsh Law firm in White Plains, which specializes in child sexual abuse cases, said her firm could be filing as many as 100 lawsuits in the coming weeks. Press reports said that as many as 500 were expected to be filed statewide by the end of last week.

One lawsuit Ms. Freeman’s firm filed included, among its seven plaintiffs, a 54-year-old man from Riverside, New Jersey. The man, a former resident of Sag Harbor, alleged that he had been sexually abused by two priests assigned to St. Andrew’s Catholic Church, the Reverend Alfred Soave and the Reverend William Burke, for six years beginning in 1973 when he was 8 years old. Because of the nature of the allegations, and his age at the time of the alleged incidents, The Press is withholding the plaintiff’s name from publication.

The lawsuit, filed in State Supreme Court in Nassau County, charges that Father Soave abused the boy from 1973 to 1976 when he was 8 to 10 years old, before Father Burke picked up and continued the abuse from 1974 to 1979, when the victim turned 14. It also names the Diocese of Rockville Centre and churches attended by the other six plaintiffs.

Besides charging negligence and causing emotional distress to the former Sag Harbor man, the suit seeks a jury trial and unspecified damages. “We are very comfortable letting the jury decide” on what the damages should be, Ms. Freeman said.

Nahid A. Shaikh, an attorney with Robins Kaplin, LLP, of New York, filed a second lawsuit on behalf of an unnamed plaintiff, identified only as ARK 27 Doe, who was a member of St. Rosalie’s parish.

That suit alleges that from 1972 to 1973, the plaintiff, who was between 8 and 10 years old, was sexually abused by the Reverend John F. Halpin. Besides the parish and diocese, the suit names five other unnamed defendants and claims all were guilty of negligence, improper training of employees and improper retention of employees. The suit also was filed in State Supreme Court of Nassau County, where the diocese is based, and it seeks a jury trial and unspecified damages.

Neither plaintiff could be reached for comment. Parishes referred all calls about the lawsuits to the diocese.

In the wake of the latest legal onslaught — at least two dozen lawsuits were filed against the church alone in Nassau County last week — the diocese issued a two-and-a-half-page press release that sought to assure victims their complaints would be heard and sought to reassure parishioners that the money they donated to their parishes or the church’s charitable arm, the Catholic Ministries Appeal, would not go toward settlement payments.

“Our church continues to suffer as a result of past sins of sexual abuse of minors,” said Bishop John O. Barres. “Victim survivors of abuse and their families also continue to carry the terrible effects of that abuse.”

“The Diocese of Rockville Centre takes seriously and investigates all allegations of sexual abuse. We commend the courage of those who have and will come forward to share their experiences and wish to see justice, healing and reconciliation prevail,” the release added. “While the ultimate effects of the Child Victims Act on the Diocese of Rockville Centre and its parishes are not yet known, and may not be known for some time, we expect the daily work of the diocese’s many ministries to continue uninterrupted. Bishop Barres and his leadership team at the Diocese of Rockville Centre have been working for months with financial and legal experts to prepare for this day.”

Spokesman Sean Dolan said the diocese would not comment beyond its press release and pointed to a separate post on its website providing information about its response to the sexual abuse scandal that has rocked the church since the 1980s and the amendments adopted earlier this year to the state’s Child Victims Act.

The church website said all allegations of sexual abuse are reported to law enforcement, and victims have been given access to counseling. The diocese also launched the Independent Reconciliation and Compensation Program in 2017. Some 370 people have filed claims and 277 of those have been settled to the tune of $50 million, according to the diocese.

Ms. Freeman said she hoped the Catholic Church was finally ready to bear responsibility for the sexual abuse scandal, but she added that church lobbyists opposed the amendments to the Child Victims Act until the day before it was passed and insisted that the law contain language clarifying that the church was not the only institution that has been caught up in a sexual abuse scandal.

“They still hold on to the secret files they have on each of these priests” who have been charged with sexual abuse, Ms. Freeman said. “They sent them away for counseling or transferred them.”