The Colorado Court of Appeals previously upheld lower court rulings against a cakeshop
The US Supreme Court is set to consider the case of a bakery that refused to sell a wedding cake to a same-sex couple.
David Mullins and Charlie Craig were told by Masterpiece Cakeshop owner Jack Phillips in 2012 that the business did not provide cakes for same-sex marriages due to his religious beliefs.
In 2015, the Colorado Court of Appeals upheld lower court rulings that "Masterpiece violated Colorado's public accommodations law by refusing to create a wedding cake for Craig's and Mullins' same-sex wedding celebration".
CBS News reports that the US Supreme Court will review that decision during its upcoming term.
Lawyers argue Mr Phillips' faith "compels him to use his artistic talents to promote only messages that align with his religious beliefs".
They add: "Thus, he declines lucrative business by not creating goods that contain alcohol or cakes celebrating Halloween and other messages his faith prohibits, such as racism, atheism, and any marriage not between one man and one woman."
In a statement, James Esseks - director of the LGBT Project at the American Civil Liberties Union (ACLU) - said: "The law is squarely on David and Charlie’s side because when businesses are open to the public, they’re supposed to be open to everyone.
"While the right to one’s religious beliefs is fundamental, a license to discriminate is not. Same-sex couples like David and Charlie deserve to be treated with the same dignity and respect as anyone else, and we’re ready to take that fight all the way to the Supreme Court."
The ACLU is representing Mullins and Craig in the case.
The Washington Post reports that a number of similar cases have arisen in the US, involving the likes of florists and calligraphers.
Last year, a bakery in Northern Ireland lost an appeal over its refusal to make a cake for a gay rights group, with the case set to be heard before the UK Supreme Court later this year.