John Bellocchio was a 14-year-old altar boy at the St. Francis of Assisi when the alleged incident occurred, NJTV News reports.
Now 37, Bellocchio claims the church covered up his case and others.
"He never would have been able to do the things he did and rise up the ranks the way he did without their complicity or consent, implied or otherwise," Bellocchio said at a news conference.
A law that was passed in New Jersey last spring and went into effect Sunday allows child sex abuse victims to sue until they turn 55 or within seven years of their first realization the abuse caused them harm.
Previously, the limit was two years.
Bellocchio's suit also names the Newark archdiocese as a defendant. Although Vatican officials are not named, the lawsuit does allege they were aware of McCarrick's behavior and continued to promote him to higher positions.
McCarrick was ordained a priest of the New York Archdiocese, and ultimately rose to the rank of cardinal.
He was defrocked last February for sexually abusing minors in the 1970s.
He is currently living at a friary in Kansas and will acquire a statement from him "as soon as possible, given his age," according to Bellocchio's attorney Jeff Anderson.
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