Advocacy group American Atheists is taking legal action to stop the 'Cross of Ground Zero' being included in the National September 11 Memorial and Museum.
They argue that the metal cross, retrieved from the wreckage of the Twin Towers, is an example of religious symbolism and part of religious history, and that including it in a publicly funded museum is therefore a violation of the separation of church and state.
If the cross is not removed, American Atheists want a memorial of a similar size made to commemorate the atheists who died in the attacks.
"The overwhelming impression of this cross is religious," said Edwin Kagin, national legal director for American Atheists, according to The Telegraph.
"We are worried about the alienation being suffered by atheists. This cross screams Christianity, but there were perhaps 500 or 1,000 people who died in this tragedy who were not Christians."
Mr Kagin claims it is "dangerous" for the cross to be included in a government-backed display.
"This is about an endorsement of Christianity," says Mr Kagin. "What is wrong with having a plaque that says 'atheists died here, too'?"
As part of an initial complaint, American Atheists claimed that their members were being made ill by the presence of the cross.
"The plaintiffs, and each of them, have suffered, are suffering, and will continue to suffer damages, both physical and emotional, from the existence of the challenged cross" claimed their initial complaint to the court, as quoted by the American Centre for Law and Justice.
"Named plaintiffs have suffered, inter alia, dyspepsia, symptoms of depression, headaches, anxiety, and mental pain and anguish from the knowledge that they are made to feel officially excluded from the ranks of citizens who were directly injured by the 9/11 attack and the lack of acknowledgement of the more than 1,000 non-Christian individuals who were killed at the World Trade Centre."
The case has been dismissed at several earlier stages, but American Atheists continue to appeal. In November 2013 the ACLJ submitted a petition with more than 230,000 signatures that supported the continued display of the cross.
The 17 foot cross is made of two steel girders and was found by construction worker Frank Silecchia amid the ruins of the World Trade Centre after the September 11 attacks in 2001.
"I was already working 12 hours. I was quite weary and the cross comforted me," Mr Silecchia said to the Religion News Service.
It is this comfort that outlined the secular purpose of this particular cross, according to Mark Alcott who represented the museum in court.
Also quoted in The Telegraph, Mr Alcott said: "The curators decided to place this object in the museum because they believe it was an important part of the history of this story. Rescue workers took comfort in this remnant of the building structure and they prayed to it as a religious object."
Speaking about the concern that people had about the objects seemingly overt religiosity, Mr Alcott said: "There is a difference between displaying an artefact of historical significance and saying we want you [the public] to bless it - museum goers understand that distinction."
On Twitter, several atheist groups used the phrase "Museums house artifacts" to outline their position. However this argument was viewed sceptically by Reena Raggi, one member of the three judge panel that will deliver a ruling on this matter.
Quoted in the National Post, Judge Raggi said: "There are countless cases of museums including religious artifacts among their exhibits and it's going to be described in a way that talks about the history of the object, what is the problem here?
"An argument has been made that you are trying to censor history."
This is a view shared by the National Association of Evangelicals, who told Christian Today that "to exclude the cross from the 9/11 story is to edit history to accommodate one atheist organisation".
"This cross is not the project of some denomination or church. It is the faith and story of women and men who served and died at the World Trade Centre," it said.
They believe the argument to remove the cross is fundamentally flawed.
"To exclude this cross because all victims were not Christians sounds like the museum should exclude the American flag because all victims were not Americans," the NAE said.
Former Ground Zero chaplain Father Brian Jordan was quoted in the Daily Mail, talking about the cross's meaning, "It is an artifact that should be included in the museum because it's a history museum. This is a part of the memory of 9/11.
"This was a sign of consolation. It's was never meant to hurt anyone, hurt the atheists or anything like that."
Eric Baxter, the senior counsel for The Becket Fund for Religious Liberty who filed a friend-of-the-court brief in the case, was quoted by the Star Phoenix as describing the American Atheists' argument as "absurd".
"We are not injured, but enriched, by remembering history as it actually happened, religion and all," he said.
The cross has been on display around the former site of the World Trade Centre for more than ten years, and has already been installed in the museum, which is scheduled to open in May after significant delays.