He also says his communications director, Peter Grimshaw, made the right decision to resign.
The opposition has been calling on the premier to front hearings in Sydney before the Independent Liquor and Gaming Authority.
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It follows claims that Mr O'Farrell promised Mr Grimshaw he would "smash" the casino and Mr Vaikunta, who was embroiled in a sexual harassment scandal with Mr Grimshaw's partner.
Asked if he would appear before the inquiry, Mr O'Farrell said: "Absolutely".
"The government will fully cooperate from top to bottom," he told reporters on Wednesday.
It is up to the authority to request him to appear.
Mr O'Farrell also repeated the claim, made to parliament on Tuesday, that he regretted Mr Grimshaw's resignation.
"I regret the whole affair. I regret that it's come to this, but as I said yesterday, Mr Grimshaw's taken appropriate action," he told reporters in Sydney's northwest on Wednesday.
"Regret is a word that's not only in the Macquarie Dictionary, but also the Concise Oxford Dictionary.
"It means what I said."
Mr O'Farrell also maintains he did not text the word "smash" to Mr Grimshaw in November 2011, when the communications director had promised his partner the premier would destroy The Star's now sacked managing director.
"Not only do I not recall them, but I don't believe they were said because the word 'smashed' for instance is not one ... term I would use," Mr O'Farrell said.
