Hobby Lobby, owned by devout Christian David Green, is embroiled in a lawsuit to gain exemption from the Obamacare mandate requiring employers to provide the morning after and week after pills as part of their health insurance plans.
The chain, which has more than 500 stores across the US, is refusing to comply with the mandate.
The case is being taken to the Supreme Court after a federal court denied a request to temporarily stop enforcement of the abortion pill mandate.
In the meantime Hobby Lobby faces daily fines of up to $1.3million per day.
Kyle Duncan, General Counsel for the Becket Fund for Religious Liberty, which is defending Hobby Lobby said: "The Greens will continue to make their case on appeal that this unconstitutional mandate infringes their right to earn a living while remaining true to their faith."
In a recent statement, Mr Green said: "These abortion-causing drugs go against our faith, and our family is now being forced to choose between following the laws of the land that we love or maintaining the religious beliefs that have made our business successful and have supported our family and thousands of our employees and their families.
"We simply cannot abandon our religious beliefs to comply with this mandate."
Purpose Driven author Pastor Rick Warren has spoken in support of Hobby Lobby, saying that the case is a battle for freedom of religion.
"Every American who loves freedom should shudder at the precedent the government is trying to establish by denying Hobby Lobby the full protection of the First Amendment," he said.
"This case is nothing less than a landmark battle for America's first freedom, the freedom of religion and the freedom from government intervention in matters of conscience."
Warren accused the US government of trying to reinterpret the First Amendment as freedom to worship rather than freedom to practise religion.
"This is not only a subversion of the Constitution, it is nonsense. Any religion that cannot be lived out … at home and work, is nothing but a meaningless ritual," he said.
He predicted that the battle to preserve religious liberty for all would become "the civil rights movement of this decade".
A Facebook campaign has been set up in support of Hobby Lobby and received over 140,000 'likes'.
The Family Research Council has said it will send a message calling for religious freedom to President Barack Obama on National Religious Freedom Day, observed each year in the US on 16 January.
