ALBANY, New York — After years of frustration and failed attempts, survivors of childhood sexual abuse prevailed Monday in Albany when lawmakers overwhelmingly voted to loosen one of the nation’s tightest statutes of limitations on molestation to give victims more time to seek criminal charges or file lawsuits.

The measure, known as the Child Victims Act, would also create a one-year litigation window for victims to file lawsuits now barred by the statute of limitations. Gov. Andrew Cuomo, a Democrat, has said he will sign the measure into law.

Long a priority for abuse victims and their advocates, the bill was blocked for years by Republicans in the state Senate. That changed last fall when Democrats won a Senate majority and the chamber’s new leader made good on her promise to put the bill to a vote. When the roll was called, the vote in the Senate was unanimous, with every Republican Senator voting yes.

“We apologize for not hearing you soon enough,” Senate Leader Andrea Stewart-Cousins, D-Yonkers, said on the floor, in what she said was a message to survivors. “We apologize for making you wait so long… The wait is over.”

New York state currently has one of the nation’s most restrictive statutes of limitations when it comes to molestation, giving victims until they’re 23 to file lawsuits or seek criminal charges against their abusers. Victims and their advocates say it often takes years or decades to speak out about abuse after it occurred.

Under the act, victims could file civil suits until age 55 and seek criminal charges until age 28. Massachusetts, another heavily Catholic state, already gives victims up to 35 years to sue. Ohio and Pennsylvania both give victims until age 30.

The one-year litigation window for past claims now barred by the statute of limitations has been the sticking point, with large private institutions such as the Catholic Church warning that it could cause catastrophic financial harm to any organization that cares for children. A similar law in California, passed in 2002, resulted in Catholic dioceses there paying $1.2 billion in settlements.

The church dropped its opposition to the act last week, however, when the act was revised to treat public and private schools and entities the same. In a joint statement on the bill’s passage, the state’s Catholic bishops said they “pray that the passage of the Child Victims Act brings some measure of healing to all survivors.”

To those victims who had pushed for passage of the act for more than a decade, Monday was cause for celebration. At a rally in the Capitol one survivor held a sign that read “16 Yrs. But we did it.”

“We faced evil forces. We faced special interests. We defeated them,” said Gary Greenberg, an abuse victim and a leading supporter of the act who created a political action committee to support candidates who backed the bill.

At least four lawmakers brought up stories of their own past abuse during legislative floor debate on the bill. Assemblywoman Yuh-Line Niou, D-Manhattan, tearfully recounted abuse she suffered at the hands of a teacher at age 13. She said the pain can be too much for any child — or adult — to bear, let alone openly discuss.

“I can still smell what it smelled like,” she said, recalling details from her abuse. Niou’s colleagues in the Assembly gave her a standing ovation before the Assembly passed the act 130-3. The Senate passed it earlier in the day 63-0.

While only three lawmakers voted against the measure, several Republicans voiced concerns that the bill could bankrupt organizations over decades-old claims that would be difficult to refute.

“For a year, you can bring a civil lawsuit against anybody with no restrictions whatsoever as to the timing,” said Assemblyman Andy Goodell, R-Chautauqua. “Your claim could be 50, 60, 70 years old. Long past the time that any individual employer would have any records to defend themselves.”

The bill was sponsored by Sen. Brad Hoylman and Assemblywoman Linda Rosenthal, both Manhattan Democrats.