McNally responded to Corden's latest comments about the alleged incident in another Instagram post on Friday, local time.
"When James Corden said in yesterday's NY Times that he hadn't done 'anything wrong, on any level', was he joking? Or was he denying being abusive to my servers?" McNally wrote.
"Whatever Corden meant, his implication was clear: he didn't do it. Although I didn't witness the incident, lots of my restaurant's floor staff did. They had nothing to gain by lying. Corden did."
McNally then extended an offer to the multi-millionaire.
"I wish James Corden would live up to his Almighty initials and come clean," he continued.
"If the supremely talented actor wants to retrieve the respect he had from all his fans (all 4 of them) before this incident, then he should at least admit he did wrong.
"If he goes one step further and apologises to the 2 servers he insulted, I'll let him eat for free at Balthazar for the next 10 years."
In his interview with The New York Times, Corden also claimed he hadn't "really read" McNally's initial explosive comments about him on social media.
"I think I'm probably going to have to talk about it on Monday's show," Corden said.
"My feeling, often, is, never explain, never complain. But I'll probably have to talk about it."
The British TV star was responding to a scathing Instagram post published by McNally earlier in the week.
"James Corden is a hugely gifted comedian, but a tiny cretin of a man. And the most abusive customer to my Balthazar servers since the restaurant opened 25 years ago," McNally wrote.
The restaurateur first claimed Corden demanded freebies and threatened the eatery with a bad review after finding a strand of hair in his food back in June.
"After eating his main course, Corden showed the hair to Balthazar manager G, who was very apologetic," he wrote alongside a snap of the comedian.
"Corden was extremely nasty to G, and said: 'Get us another round of drinks this second. And also take care of all of our drinks so far. This way I (won't) write any nasty reviews in Yelp or anything like that.'"
In another incident that allegedly took place on October 9, McNally claimed Corden lashed out at his staff after the dish his wife, Julia Carey, ordered was not prepared in the way she had requested.
"Mr Corden's wife ordered an egg yolk omelette with gruyere cheese and salad. A few minutes after they received the food, James called their server, M.K and told her there was a little bit of egg white mixed with the egg yolk. M.K informed the floor manager, G. The kitchen remade the dish but unfortunately sent it with home fries instead of salad," the post continued.
"That's when James Corden began yelling like crazy to the server: 'You can't do your job! You can't do your job! Maybe I should go into the kitchen and cook the omelette myself!'"
McNally claimed the server was "very apologetic" and brought the manager over who gave the couple free glasses of champagne to ease tensions. The manager reported that Corden was pleasant to him but "nasty" to the server.
"I don't often 86 a customer, (but) today I 86'd Corden. It did not make me laugh," McNally wrote at the end of the post.
The term "86" is culinary slang that refers to nixing unavailable menu items or, in this case, customers who are no longer welcome.
The public naming and shaming of the star quickly went viral and reportedly prompted Corden to reach out to McNally personally apologise, according to the restaurant owner.
McNally said Corden called him to apologise "profusely" for his behaviour, which led him to revoke the ban.
Whether the ban will be reinstated remains to be seen.
