Following Florida's legalisation of same-sex marriage this week, the Archbishop of Miami has warned diocese employees that that they risk being fired if they show support for gay marriage, including comments made online.

Archbishop Thomas Wenski wrote a letter to all staff reminding them that whatever their role within the diocese, they are representatives of the Catholic Church and should abide by its teaching, the local NBC station reports.

The letter included excerpts from the staff handbook which said that employees should "conduct themselves in a moral and ethical manner consistent with Catholic principles" at all times.

It also said: "All employees should note that, because of the Church's particular function in society, certain conduct, inconsistent with the teachings of the Catholic Church, could lead to disciplinary action, including termination, even if it occurs outside the normal working day and outside the strict confines of work performed by the employee for the Archdiocese."

The handbook explicitly refers to what staff say online: "Employees should exercise discretion when posting on social media sites, and note that online activity indicative of prohibitive behaviors may subject an employee to disciplinary action or termination."

Same-sex marriage was legalised in Florida on Tuesday after a court ruling by a district judge that overturned the state's ban. Gay marriage is now recognised in 36 US states.

Florida's Catholic bishops released a joint statement in response to the change in the law expressing their disappointment with the judge's decision.

"In redefining marriage to include same sex couples, the judge has in effect overturned a state constitutional amendment approved by nearly 62 per cent of the electorate in a 2008 ballot initiative," the statement said.

"Marriage based on the complementarity of the sexes is the lifeblood of family, and family is the foundation of our society. The crisis that sadly the family is experiencing today will only be aggravated by imposing this redefinition of marriage. Society must rediscover the irreplaceable roles of both mother and father who bring unique gifts to the education and rearing of children."

However, within the Catholic Church in the US views on same-sex marriage differ. A Pew Research Center survey last year showed that young Catholics in particular were more inclined to support same-sex marriage, including up to 75 per cent support among those aged 18-29. But even among Catholics aged 65 and over, 38 per cent said they were in favour of same-sex marriage.