The Westbury Village Board of Trustees said it would not act Thursday night on an application from the Post Avenue nightclub Avanti, which was seeking a special-use permit to operate as a cabaret bar.
Mayor Peter Cavallaro did not say when the board would decide.
The nightclub was effectively shut down by the village board last month after it voted not to renew its special-use permit, citing noise and garbage complaints and an advertisement the mayor claimed promoted a "swingers party."
The online advertisement, provided by the village, used the phrase "Start Your Sexual Revolution" and "Swing Life Style."
Cavallaro said the club violated an "adult uses" covenant.
Representatives for the club denied any sexual activity took place during the club's events.
An attorney for club owner Barry Ceriano denied that such an event was held at the night club and said the owner was unaware it was being advertised that way by a promoter.
At times, the exchanges between Cavallaro and the club's attorney were impassioned.
"It was a promoter that he could not control," said the attorney, Sherman Jackson, of owner Ceriano.
"He is the person in control of the premises," Cavallaro countered.
Cavallaro added: "The law is clear, adult uses are permitted in the village in certain areas; they're not permitted in the establishment that he's operating."
Cavallaro said the club violated other components of the covenant, saying the club failed to report various police calls to the village.
One resident who lives nearby, Nick Martone, said he often calls the police because of disruptions, but said, "they don't come."
Other residents, wary since a new performing arts center is set to open, raised concerns about traffic on Post Avenue.
"On a Friday night, I can't drive down Post Avenue," said Ellen Hurwitch, 58, who has lived in the village for nearly 12 years. But she added, "If it's run properly, it's fine."
After the hearing, Cavallaro said the board is "cognizant of the rights he [Ceriano] has as a business owner" and will take them into account when deciding. If the permit were renewed, he said, it would likely be stricter.