Sheriff’s deputies said Mr. La Rosa-Lopez was released from jail on Thursday morning. Attempts to reach him Thursday night were unsuccessful. Jail records indicated Wednesday that he was being held with bail set at $375,000.

In a statement, the Conroe Police Department said it took two separate reports of sexual abuse by Mr. La Rosa-Lopez last month. The reports alleged that over a span of several years in the late 1990s and early 2000s, Mr. La Rosa-Lopez sexually abused children while he was at Sacred Heart Catholic Church, which is in Conroe.

The police began an investigation last month and issued a warrant for Mr. La Rosa-Lopez, who they say turned himself in on Tuesday.

Although the allegations are connected to episodes that are almost two decades old, Texas lawmakers, in 2007, removed the statute of limitations for cases of indecency with a child, so those cases can still be prosecuted.

Mr. La Rosa-Lopez is listed as the pastor at St. John Fisher Catholic Church in Richmond, Tex. — one of the Archdiocese of Galveston-Houston’s more than 140 parishes — a position he has held since 2005. The church is 70 miles from where the abuse allegedly took place.

Cardinal DiNardo was not named archbishop of Galveston-Houston until 2006, according to the archdiocese’s website. But he took a meeting in 2011 with one person who accused Mr. La Rosa-Lopez of abuse, and met with another accuser in August 2018 in a separate case involving the priest.

A spokesman for the archdiocese said on Thursday that Mr. La Rosa-Lopez was removed from St. John Fisher about three weeks ago because of the allegations. “He is not permitted to exercise any ministry,” the spokesman, Jonah Dycus, said.

In a statement, the archdiocese said that in 2001, officials were told by a 16-year-old girl and her family that the priest “had kissed and touched her inappropriately” when he was the parochial vicar at Sacred Heart. It said the officials reported the information to Children’s Protective Services, adding that Mr. La Rosa-Lopez denied touching the girl inappropriately.

Mr. La Rosa-Lopez was briefly reassigned to another church in May 2001 while the allegations were being reviewed, Mr. Dycus said. Mr. La Rosa-Lopez then entered a residential treatment program, Mr. Dycus said, before being assigned to administrative duties for about three years and then being sent to St. John Fisher.

An affidavit filed on Monday said a female victim told the police that after she learned of Mr. La Rosa-Lopez’s 2010 appointment as vicar for Hispanics by Cardinal DiNardo, she contacted the church. The archdiocese said it held four meetings with her between 2010 and 2011, and at the final meeting, which the cardinal attended, Mr. La Rosa-Lopez apologized and expressed remorse.

Then, in an interview on Aug. 10 of this year, a 36-year-old man told Cardinal DiNardo that Mr. La Rosa-Lopez sexually abused him from 1998 to 2001, when the man was a high school student and Mr. La Rosa-Lopez was assigned to Sacred Heart. The archdiocese said that, once again, it reported the allegation to Children’s Protective Services. And once again, Mr. La Rosa-Lopez denied the allegations.

“Such behavior simply will not be tolerated,” the archdiocese said. “To anyone affected by any form of abuse by anyone who represents the Church, the archdiocese deeply regrets such a fundamental violation of trust, and commits itself to eliminating such unacceptable actions.”

Following Mr. La Rosa-Lopez’s arrest, critics questioned why Cardinal DiNardo continued to allow the priest to minister after being made aware of the sex abuse allegations. Both victims told the police they were motivated to file reports because of the media reports on the sex abuse scandal involving the Catholic Church. One said she was motivated by what she perceived to be Cardinal DiNardo’s “duplicity.” (Cardinal DiNardo has, for instance, expressed shame and remorse over a grand jury report on clergy sex abuse in Pennsylvania.)

Neither person who filed a report could be reached for comment.

“We simply do not understand this callous disregard for the safety of children by Cardinal DiNardo and other Houston Church officials,” Mr. Norris said in a statement for the survivors network.