Rugby Australia (RA) boss Raelene Castle has defended the governing body's settlement with Israel Folau as a "commercial decision" and necessary to avoid the cost and distraction of testing its inclusion policy in court.

RA and Folau announced on Wednesday they had settled their unfair dismissal case, ending a long and bitter dispute after the former Wallaby was sacked in May for posting a meme on social media that hell awaits "homosexuals" and other groups.

The settlement has drawn criticism from some media pundits, who have viewed it as a humiliating surrender by RA and called on chief executive Castle to resign.

Castle, however, said she had no intention of quitting and the settlement was in the best interests of the game.

"We didn't back down," Castle told reporters at RA's Sydney headquarters on Thursday.

"We needed to give the game cost certainty.

"These are ultimately commercial decisions ... We stick to our values that inclusiveness is absolutely core to the game of rugby. Ultimately, taking this conversation further into a court situation was not helping the game."

RA apologised to Folau and his family in a statement on Wednesday. Folau, who had been seeking compensation of A$14 million, apologised for "any hurt or harm caused to the game of rugby."

The terms of the settlement were undisclosed but one local newspaper said it included an A$8 million pay-out for the 73-test Wallaby.

Castle said the numbers reported by local media were wrong and defended the apology.

"That apology was both ways because this has been very stressful, it's been a very hard time for the Folaus. It's been a very hard time for Rugby Australia," said the New Zealander.

"At the end of the day it was about that difficult time that Rugby Australia apologised for but we stand by our decision."

Folau said in a video message on Wednesday that he was "vindicated" and "extremely pleased" with the settlement.

Folau had also sought to have his Wallabies contract reinstated in his statement of claim to the Federal Circuit Court, but Castle said she could not see him returning to the game in Australia.

"I think it's clear to see that our values are not aligned and the expectations that Rugby Australia would have of Israel coming back into the sport would not be acceptable to him," she said.