ALBANY — Supporters of the emotion-packed, decadelong effort to eliminate the statute of limitations on child sexual abuse are trying to seize a last chance this legislative session to empower adults to pursue charges and damages against their abusers even decades later.

Supporters of the measure, introduced by Sen. Brad Hoyman (D-Manhattan), are pressuring Gov. Andrew M. Cuomo to muscle the measure out of the Senate to a vote by the scheduled end of the session on June 21. On April 20, the Republican-led Senate used a procedural measure to move the bill into the Rules Committee, headed by Senate Majority Leader John Flanagan (R-East Northport), who has the power to move the bill to a floor vote.

“The fact is that the governor can create the political will, or he can abandon the force of his own words and pass the blame of his inaction onto the Senate,” said advocates Kat Sullivan and Birdie Farell in a written statement.

Cuomo noted through a spokesman that the bill isn’t progressing through the legislature.

“We continue to work with the advocates to build the political support to get it passed, which does not exist at this time,” Cuomo spokesman Rich Azzopardi said.

The Child Victims Act would lift the current statute of limitation that requires a criminal or civil case be brought within five years of the incident. It also would eliminate the current provision in law that requires criminal cases to be brought within three years of a victim’s 18th birthday.

The proposal also would provide a one-year period during which people over 23 years of age could bring a civil case.

An alternative bill is making some progress in the Senate and Assembly and has support from the Catholic Church. That would eliminate the statute of limitations for criminal prosecution but would extend the window for civil lawsuits from five to 10 years. It also makes members of the clergy legally obligated to report abuse.

Victim advocacy groups such as Safehorizon and Catholic Whistleblowers, armed with some academic research, argue that victims often are unable to fight through the trauma until adulthood, if then.

“I didn’t go public until I was 50,” said Robert Hoatson, a former priest, in a recent news conference held by advocates of the Child Victims Act. Hoatson said he was abused from age 3 to 29 and now works for a victims’ group in New Jersey. “There is no statute of limitations on the murder of the body. Why is there a statute of limitations on the murder of the soul?”

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Former Suffolk County Police Det. Rory Forrestal recalled getting an abuser to confess that he buried photos of his victims in his backyard from years before.

“I have to go back to the victims’ families and say I have evidence, but I can’t do anything about it,” he said. He had found nearly 30 photos.

The bill remains mired in committee in the legislature. The bill’s sponsor, Hoyman, accuses the Senate’s Republican majority of freezing it.