NEW YORK — In 2009, Augusto Cortez, a Roman Catholic priest, pleaded guilty to forcible touching of a 12-year-old girl in Brooklyn. He was sentenced to six years probation, but was allowed to remain a member of his religious order.

Last year, a couple in Hampton Bays, on Long Island, who had known Cortez for years accused him of molesting one of their daughters, now 8. He was interviewed by the Southampton Town Police and released, but he quickly vanished and became a fugitive, the authorities said.

On Monday, the Hampton Bays family sued Cortez’s Catholic order as well as the Roman Catholic Diocese of Rockville Centre, where he had worked, alleging they had been “negligent, careless, and reckless” in failing to properly train and supervise Cortez, 52, and to warn the family about his “propensity to sexually molest youth.”

The family’s lawyer, Michael Dowd, said in an interview: “To let this guy run around is crazy. It points to the fact that they’re still not taking this stuff seriously.”

A spokeswoman for the regional division of the order, the Congregation of the Mission, denied the allegations of negligence and said, “We will respond to these issues in court.”

Sean Dolan, a spokesman for the Diocese of Rockville Centre, said diocesan officials had not yet seen the complaint and could not comment.

According to the lawsuit, which was filed in state Supreme Court in Queens, the Hamptons Bay family met Cortez in about 2004 at the First Communion of their elder daughter.

Cortez and the family developed a close friendship. The priest helped the family get a mortgage to buy a house, and he was an occasional visitor there, conducting Mass and blessing meals, Dowd said.

“This guy insinuated himself into the family and he made it his business, as most abusive predators do, to become very close to the family,” the lawyer said.

In June 2008, Cortez was indicted by a grand jury on several charges, including second-degree sexual abuse and forcible touching, for allegedly fondling a 12-year-old girl’s breasts when he was alone with her in the computer room of a Catholic parish school in Brooklyn, according to the lawsuit. He pleaded guilty in May 2009 to the forcible touching charge, a misdemeanor, which required him to be registered with the state as a sex offender.

In June 2009, before the plea deal was made final, his religious order put into place a “Personal Safety Plan” for him that limited his activity, the lawsuit said. The plan laid out a program of rehabilitation and supervision for the priest, requiring regular therapy sessions and supervisory meetings, and it restricted his access to children.

The order also removed him from active ministry and barred him from performing any priestly functions.

“He is not permitted to be alone with any minors male or female,” the lawsuit said, quoting the safety plan. “He is not permitted to be involved in external public ministry nor present himself as a priest.”

Despite the plan, Cortez’s visits with the family continued after his conviction, the lawsuit contended.

After the priest’s arrest in 2008, according to the lawsuit, the plaintiff’s mother sought the counsel of a priest of Cortez’s order who worked at a parish church in the Diocese of Rockville Centre. He told her that whatever had transpired between Cortez and the girl in Brooklyn “was just an accident,” the lawsuit contended, without naming the priest.

The girl’s mother accepted the priest’s interpretation, the lawsuit said, and “believed it was safe for her and her family” to continue their friendship with Cortez, who, like the girl’s parents, are from Guatemala.

Until last year, the suit said, Cortez was an occasional guest at the family’s house in Hampton Bays, blessing meals, conducting Mass, and giving sermons, despite the safety plan that forbid him from public ministry.

According to Dowd, the family did not learn about Cortez’s sexual-abuse conviction until late last year and were never told about it by the diocese or the order.

Dowd contended that Congregation of the Mission and the diocese “had a duty to warn any family that had a relationship with Cortez that he was a sexual predator.”

The parents declined a request for an interview.

The spokeswoman for Congregation of the Mission, Suzanne Halpin, said the order “is not knowledgeable as to the relationship, if any, between the family and Mr. Cortez.”

“We have no knowledge that he continued to conduct himself in ministry,” she added.

Halpin also said officials with the order were “aware of nothing that supports” the mother’s allegation that a priest had dismissed her concerns after the arrest in 2008.

In June 2014, the family invited Cortez to their home for a party celebrating their elder daughter’s graduation from high school. At one point, the mother walked in on Cortez and her younger daughter alone in a room, the lawsuit said. As she entered, she saw Cortez zipping up his pants, Dowd said.

The girl’s mother called the Southampton Town Police, who interviewed Cortez before releasing him. He soon vanished, and, according to the US Marshals Service, he is being sought on charges of first-degree sexual abuse, endangering the welfare of a minor, and a first-degree criminal sex act.

As of Monday, Cortez remained a fugitive; the authorities believe he fled the country.

In September, he was expelled from his order, which has petitioned the Vatican to remove him from the priesthood, Halpin said. The request is pending.