ALBANY, N.Y. — New Yorkers who were molested as children joined lawmakers and advocates in a two-day rally for lifting the state’s statute of limitations on suing abusers, saying the current law closing the window for such lawsuits at age 23 guarantees many more young victims.

Their effort has faced years of opposition from the Catholic Church and other institutions, who charge that litigation related to crimes committed decades ago could cripple operations in the present serving the poor and other disadvantaged groups.

Lawmakers said prospects are improving for passing the bill with a recent change in legislative leadership in Albany. They also cited Massachusetts’ passage two years ago of a similar measure, and the recent Academy Award-winning film “Spotlight” about priests sexually abusing boys in Boston.

The film was being shown Wednesday near the Capitol.

“I think we have some movement on the bill,” Assemblywoman Margaret Markey said Wednesday. The Queens Democrat has repeatedly introduced legislation that hasn’t advanced, but which currently has 61 co-sponsors in the 150-seat Assembly.

Assembly Speaker Carl Heastie, a Bronx Democrat, has said the bill will be discussed in the majority Democratic Conference this year, a spokesman said Wednesday. The legislative session ends in June.

A dozen victims who spoke at an earlier forum recounted sex abuse by youth coaches, Catholic and Jewish clergy and older family members. Most said it took years into adulthood to even begin to process what happened and that the scars are lasting.

While the lawsuits claim emotional, physical and psychological harm, the more critical point is to identify publicly serial predators and to stop them from hurting more children, several victims said.

“Children have a right to be protected,” said Kathryn Robb, a legislative advocate of Massachusetts Citizens for Children.

A 2014 law enacted there expanded the window for civil suits against individual abusers for victims aged 21 to 53. However, it doesn’t similarly allow victims over 21 to retroactively sue their abusers’ supervisors or institutions that employed them, something done to overcome Catholic bishops’ opposition.

Markey’s legislation would end New York’s statute of limitations for bringing civil lawsuits against sex predators of victims under 18. It would also establish a one-year lookback where cases could be brought for abuse years ago.

Sen. Brad Hoylman, a Manhattan Democrat, has introduced a companion bill that would also allow such suits against public institutions, including schools and state and local governments, addressing one of the arguments by private institutions that they were unfairly singled out.

A spokesman for the Senate’s majority Republicans said Wednesday they’re reviewing the bill.

The New York State Catholic Conference said it supports increasing the statute of limitations on child sexual abuse, both criminally and civilly, going forward, but opposes legislation that would reopen claims from decades ago, spokesman Dennis Poust said.

Both Markey and Hoylman declined Wednesday to back off on enabling lawsuits against institutions. Their cover-ups enabled the abuse and protected predators, Markey said.

Females are the most frequent victims, though gay, lesbian and disabled children are also frequently targeted, said Marci Hamilton, a legal scholar and author. She tracks the issue in 50 states on a website called About one-third of cases involve abuse by older minors, and 37 states have no statute of limitations on criminal prosecutions for child sex abuse, she said.

Her research shows New York’s law among the most restrictive, while several states — California, Delaware, Minnesota, Hawaii, Connecticut, Massachusetts and Georgia — have enacted various laws in the past 15 years to expand time frames for victim lawsuits.