The decision to take the so-called "gay cake" case to the European Court of Human Rights has disappointed Christian campaigners.
The owners of Ashers bakery in Belfast won a Supreme Court appeal last year over a claim that they had discriminated against a customer by refusing to make a cake iced with a pro-gay marriage message.
Now that ruling is to be challenged, on the basis that it "failed to give appropriate weight" to the human rights of Gareth Lee, who first brought legal action.
Mr Lee, a gay rights activist, claimed he had been discriminated against when the firm refused to make him a cake bearing the slogan "Support Gay Marriage".
Lawyers from Phoenix Law, acting for Mr Lee, said: "The latest legal battle does not directly implicate the owners of Ashers Bakery or challenge their right to privately hold religious/political views.
"Instead the case will be against the United Kingdom, a member state to the European Court."
Mr Lee said: "I'd fight for the rights of business owners to be able to hold their own religious beliefs. I have my own beliefs.
But that's not what my case has ever been about. This is about limited companies being somehow able to pick and choose which customers they will serve. It's such a dangerous precedent.
In October last year five justices at the UK's highest court allowed a challenge by the McArthur family, who run the bakery in Belfast, in a unanimous ruling in London.
Mr Lee initially won his case in the county court and then at the Northern Ireland Court of Appeal, but the McArthurs then challenged those rulings at a Supreme Court hearing in Belfast in May.
The Christian Institute has branded the latest legal action "an attack on freedom of expression, religion and belief" and said the Supreme Court ruling "must be robustly defended".
The group's deputy director Simon Calvert said: "I'm surprised and a little disappointed that anyone would want to overturn a ruling that protects gay business owners from being forced to promote views they don't share, just as much as it protects Christian business owners and hope the Government will robustly defend the current law."
Controversy first flared when Mr Lee, a member of the LGBT advocacy group QueerSpace, ordered a £36.50 cake in 2014 featuring Sesame Street puppets Bert and Ernie for a private function marking International Day Against Homophobia.
His order was accepted and he paid in full but, two days later, the company called to say it could not proceed due to the message requested.
