The former Australia full-back had his contract terminated after an investigation into an offensive social media post in April.
Folau, a devout Christian, uploaded an image to Instagram that said "hell awaits drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolators".
The 30-year-old had been warned for similar comments last year and was this time found guilty of a "high-level breach" of the governing body's code of conduct.
Folau opted not to appeal against RA's decision, but his legal team filed applications with the Fair Work Commission this week and he is reportedly seeking up to $10 million in damages.
A letter reportedly sent by Folau to RA's board members in which he accused the governing body of leaking details of his Code of Conduct hearing to the media came to light on Saturday.
But RA hit back with a statement, which read: "While we accept that a PR firm has been engaged to coordinate a media campaign to promote the legal action taken against Rugby Australia, we are disappointed that this campaign is impacting on the work done by the thousands of volunteers who are delivering great experiences for the Rugby community and also that it has taken the focus away from a crucial Australian Super Rugby derby, being played by Israel's former team [NSW Waratahs].
"Rugby Australia has acted with complete professionalism and integrity at all times through the process in which Mr Folau was found by an independent three-member tribunal panel to have made multiple, serious breaches of the Professional Players Code of Conduct.
"While we will continue to respond to any legal action as required and will continue to defend the values that underpin our game and the work done by the hard working volunteers, we will not engage in a running media commentary."