A federal appeals court told the American Atheists on Thursday that they must provide more evidence if they want to purport that the "Ground Zero cross" is offensive.
The atheist organization first filed suit in 2011, stating that the cross violates the Constitution's freedom of religion protections. The suit was thrown out last year.
The cross is a 17-foot tall, steel structure that was found in the rubble of the World Trade Centers after 9/11. First responders prayed and left messages or gifts at the cross, and the symbol later became a tourist attraction. The cross is currently part of the National September 11 Memorial & Museum.
The appeals court gave the plaintiffs until July 14 to supplement their claim with proof of how the cross is a "constitutional injury," and "marginalizes them as American citizens," according to Fox News.
They also need to show how the monument shows "particular and concrete injury" rather than "the abstract stigmatization of atheists generally."
The decision followed a legal opinion submitted by the Becket Fund for Religious Liberty.
Becket Fund attorney Eric Baxter applauded the court's decision to ask for more evidence.
"We're thrilled that the court picked up on this issue," he told Fox News.
"Courts should not allow people to sue just because they claim to get 'dyspepsia' over a historical artifact displayed in a museum.
"Taking personal offense is not an injury that warrants invoking the power of the courts to shut down everything you disagree with," he continued. "The Constitution is not a personal tool for censoring everyone's beliefs but your own."
The Memorial & Museum were erected to honor the memories of the 3,000 people killed in the 1993 and 2001 terrorist attacks, and opened on May 21.
The American Atheists also claim that the Museum uses tax dollars, and therefore cannot have religious mementos. 9/11 Foundation CEO Joe Daniels has said that the projects were self-funded.