Fr Tim Bartlett was responding to an Equality Commission decision to take a civil action against a Christian-owned bakery firm.
Earlier this year, Ashers Baking Company refused to bake a cake with a pro-gay marriage slogan.
Fr Bartlett was on the panel of this year's Belfast Pride event.
He is a member of the Catholic Council for Social Affairs.
On Thursday, he issued a statement to BBC's Nolan Show saying: "I will be writing today to those groups from the gay community, with whom I have had a very constructive and ongoing engagement in recent years, to say that I am withdrawing my engagement until the right of all people, in this case Christians, to freedom of conscience is vindicated and respected by the Equality Commission and the gay community.
"I also want to know why the chief commissioner of the Equality Commission talked quite openly about the Ashers case during the Gay Pride debate in Belfast but has since claimed he is not free to talk about it in public debate."
Later, speaking on The View programme on BBC Northern Ireland, Fr Bartlett said he wanted the gay community to "respect my right not to be coerced, not to be forced to do something against my conscience in society".
John O'Doherty of the Rainbow Project, a health support group for gay, lesbian, bisexual and transgender people and their families, criticised Fr Bartlett's comments.
"I think it's very disappointing. I think rather than being a reason to stop conversations, it further indicates the needs for conversation," he said.
"There are fundamental issues that need to be addressed and these need to be discussed, the answer isn't to walk away and say until you agree with me I'm not going to bother talking to you'."
Rev Dr Norman Hamilton of the Presbyterian Church said he was deeply concerned by the Equality Commission move.
"In a situation where a business has clearly stated that it is willing to serve any customer irrespective of religion, sexual orientation or political belief, it surely is totally unjust to attempt to compel it to be involved in promoting causes which in conscience are against the owners' strongly held Christian beliefs," he said.
"This is a deeply regrettable failure of civic leadership by the Equality Commission."
The row hit the headlines in July, when the baking company revealed it was facing possible legal action over its decision to decline the customer's request.
The cake had been ordered in Belfast by a gay activist two months earlier, for a civic event in Bangor, County Down, marking International Day Against Homophobia and Transphobia.
Ashers Baking Company said it had declined the request because it was "at odds" with its Christian beliefs.
In a letter sent to the bakery last week, the Equality Commission said that unless the firm acknowledged there had been a breach in the equality laws and offered recompense, it would start legal proceedings.
The commission said its correspondence with the company "made clear that the claimant will be seeking only modest damages for the upset and inconvenience caused".
However, the letter warned the firm that "failing this, a civil bill will be issued".
In a statement on Wednesday, the commission said it had now received a reply from the bakery's solicitors "stating that their view remains unchanged, that their clients have not acted unlawfully".
The watchdog said it "would prefer not to have to litigate" but added the case "raises issues of public importance regarding the extent to which suppliers of goods and services can refuse service on grounds of sexual orientation, religious belief and political opinion".
The commission added that any decision as to whether or not discrimination had occurred would be "a matter for the court".
In a statement posted on the Christian Institute's website, the bakery firm's general manager said they were surprised the case was still being pursued.
A priest has said he will withdraw engagement with groups from the gay community until the right of all people to freedom of conscience is respected.