Folau and his legal team met with RA at the Fair Work Commission in the first formal step of his unfair dismissal case but there was no resolution after a nearly four-hour hearing.
"It appears as though, unless things change, that we will be heading to court," Folau's solicitor George Haros told reporters.
Folau said: "Very, very disappointed about the outcome today but I'd like to thank all those that have supported me throughout this time and I'll continue to stand up for the freedoms of all Australians."
Folau's four-year contract for Australia and Super Rugby team New South Wales Waratahs was torn up last month after he was found guilty of a "high-level" breach of RA's code of conduct for posting on social media that hell awaits 'drunks, homosexuals, adulterers' and other groups.
RA and the state governing body New South Wales Rugby Union said they were "incredibly disappointed" that the conciliation hearing had failed.
"We remain confident in our processes and will continue to do what is required to defend the values that underpin our game," they said in a statement.
The FWC's conciliation hearing offers a last chance for employers and employees to settle a dispute before taking proceedings further.
Before arriving at the hearing on Friday, Folau told reporters he wanted: "Hopefully an apology from Rugby Australia. That would be great."
The 30-year-old is seeking A$5 million ($3.50 million) plus compensation for foregone sponsorship and future contract income from RA in a case he has cast as a fight for 'religious freedom'.
Backed by a Christian lobby, Folau raised a warchest of A$2 million from thousands of public donors in two days and has said he will take the case to Australia's highest court if unsuccessful.
An apology from RA was never a likely outcome of the hearing, however, with CEO Raelene Castle doubling down on the governing body's position that Folau's case was an 'employment' matter not a religious one.
"I want to make clear that Rugby Australia has acted with complete professionalism and integrity at all times through the process by which Israel was found, by an independent three-member tribunal panel, to have made multiple, serious breaches of the Professional Players Code of Conduct," Castle said on Thursday.
The cash-strapped governing body is also under pressure from sponsors to hold firm on Folau, with Qantas, the airline that holds naming rights to the Wallabies, 'very supportive' of RA's actions.
Former Wallaby Mark Gerrard said the legal case was a distraction Australian rugby could ill afford and one that would harm the legacy of a 73-test player who won the nation's top award, the John Eales medal, a record three times.
“Unfortunately his rugby reputation is going to be tainted in a different picture, which is very unfortunate for him because he was a great footballer for us," Gerrard told local media.
With the showpiece Rugby World Cup starting in less than three months, RA and Folau were urged to settle quickly for the good of the game by a prominent rugby executive.
"You can die for a principle or be pragmatic. No one is going to win here," New South Wales Rugby chairman Roger Davis said in comments published by the Sydney Morning Herald.
"It is in the best interests of the game to mediate a solution to this, but it will require both sides to move off their preferred position."
(Reporting by James Redmayne; Writing by Ian Ransom; Editing by Sudipto Ganguly/Peter Rutherford)
