MADISON, Wis. — A Wisconsin group that advocates for the separation of church and state sued Congress on Thursday after its co-president was barred from giving an opening invocation before the U.S. House.

The lawsuit alleges that House Chaplain Patrick Conroy rejected an application from Dan Barker, co-president of the Madison-based Freedom From Religion Foundation, to deliver a secular guest invocation in January. The foundation says Conroy wrote that Barker, an atheist and former Christian pastor, wasn’t a true “minister of the gospel.”

The suit argues that Conroy violated Barker’s constitutional rights and the 1993 Religious Freedom Restoration Act, and that Conroy’s requirements disparately burden nonreligious and minority groups. The suit notes that nearly 97 percent of invocations given to the House over the past 15 years were delivered by a Christian chaplain or guest Christian chaplain.

The U.S. House Chaplain’s office directed inquiries about the lawsuit to U.S. House Speaker Paul Ryan’s office, where a spokesman didn’t immediately respond to a call and email seeking comment. Barker had secured sponsorship to deliver an invocation from Democratic Rep. Mark Pocan of Wisconsin.

The lawsuit was filed in U.S. District Court in Washington on the National Day of Prayer, an annual day of observance initiated in 1952 that the foundation unsuccessfully tried to strike down in a 2008 lawsuit.

The foundation’s co-president, Annie Laurie Gaylor, acknowledged the new case will be an uphill fight.

“This is a hard case to take and win — we know that,” Gaylor said. She said Conroy’s action “was really very insulting.”

According to the complaint, less than 3 percent of House invocations have been delivered by Jews in the last 15 years, and less than half of a percent by Muslims or Hindus. No atheist or agnostic invocations have been given, according to the complaint.

In comparison, more than a fifth of Americans are religiously unaffiliated, according to the Pew Research Center.

“There is nothing inherent in atheism, Jainism, Rastafarianism, Buddhism, or any minority religion known to the plaintiffs that would prohibit their leaders from performing the duties of the guest chaplain,” the lawsuits states.