Folau, a devout Christian, had his contract terminated by RA and the Waratahs for a "high-level breach" after he posted "hell awaits drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolaters" on Instagram.
RA and Folau failed to reach a settlement in June over the full-back's sacking and an unfair dismissal case began in court on Tuesday.
Solicitor George Haros, representing Folau, said his client is "extremely strong" and is keen for an apology as he addressed the media outside court.
"It's been publicly acknowledged by Israel and his team that he still seeks that apology, and that's still very important to him," Haros said.
"[It would] come a long way to resolving the dispute.
"Obviously Israel's very forthright in his views and he's extremely strong at this stage of proceeding."
RA has filed an application for the case to be heard by the federal court, which Folau's barrister Stuart Wood suggested had "no merit and will only lead to delay and increased costs".
"We are conscious that there are going to be attempts to further delay the rights of my client to have this matter quickly dealt with," he said.
The allegation was denied by RA lawyer Adam Hochroth.
The case will go to mediation in December, but if a resolution is not found the parties could face trial in February.
Photo Getty Images. Caption: Former Australia full-back Israel Folau