(Reuters) - Five U.S. men who say they were sexually abused as minors by Roman Catholic priests filed a federal lawsuit in Minnesota on Tuesday against the Vatican, accusing the church of concealing the identities of thousands of predator clergy members.

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Three brothers and two other men claimed in a lawsuit filed in U.S. District Court in St. Paul that the Church has kept secret the identities and records of more than 3,400 clergy accused of sexual abuse, including some top church officials.

The men are asking the court to require the Vatican to make the information public and report all alleged crimes to law enforcement worldwide.

Allegations of rampant sexual abuse of minors by priests and subsequent cover-ups by bishops exploded onto the world stage in 2002. The scandals have cost the church billions of dollars and undercut its moral authority.

The three brothers in the lawsuit say they were molested by former Minnesota priest Curtis Wehmeyer between 2006 and 2012. The lawsuit says another plaintiff was sexually abused by former Minnesota priest Thomas Adamson in the early 1980s, and that the fifth man was molested by former priest Fidencio Silva-Flores in California sometime between 1978 to 1984.

Wehmeyer pleaded guilty in 2012 to 20 criminal counts against him stemming from the sexual abuse and possession of child pornography. He was sentenced to five years in prison.

Adamson, who faced accusations of years of abuse and was removed from the priesthood, died recently. Silva-Flores was charged with 25 counts of child molestation in 2003 but never tried. As of 2002, Silva-Flores was working in a church in Mexico, according to the lawsuit.

In 2014, the Vatican reported that since 2004, more than 3,400 cases of abuse worldwide had been referred directly to Rome. According to the Vatican, 3,420 clergy involved in those cases were removed from ministry, but their names and cases have never been made public, the lawsuit said.

The Vatican figures may not capture the full picture. The U.S. Catholic Conference of Bishops has indicated that more than 6,000 clerics in the United States alone have been accused of sexual abuse of minors between 1950 and 2016.

Not all the names have been released. But several U.S. dioceses in recent months have identified former bishops, priests and deacons who were accused of sexually abusing children.

A week ago, Pope Francis issued a landmark decree making bishops directly accountable for sexual abuse or covering it up and requiring clerics to report any cases to Church superiors.

In the United States, state and federal authorities have been investigating how the church handled decades of allegations of sexual misconduct by priests, and at least nine sexual abuse lawsuits have named the Vatican as a defendant in recent years. Two other cases filed this year in Guam and Washington are in early stages.

Many other cases were dismissed due to a lack of jurisdiction as it is difficult in U.S. courts to sue a foreign state like the Vatican.