In a terse statement, conservancy officials, who declined an interview request, said they had “dialogue’’ with the city about the event and had “expressed our serious concerns,” but that “ultimately the Parks Department granted the permit which is in its sole authority to do.”

But organizers defended the festival, which will feature music by John Legend, food by celebrity chefs like Marcus Samuelsson and Rachael Ray and comedy by Trevor Noah, pointing out that they are only charging for half the tickets and the rest will be free. About 40,000 people are expected each day of the festival.

Though they have a permit from July 15 through July 24 that bars other officially permitted activity on the Great Lawn, OZY Fest organizers say they will keep much of the space open for much of that time.

The festival is “a truly unique blend of thought leadership alongside incredible music, comedy and food,’’ said Samir Rao, vice president of operations for OZY Media, which is producing the festival.

The ticket prices range from $69 for single-day admission to $399 for V.I.P. weekend passes. Free tickets will be distributed to students, teachers, military veterans and other groups, Mr. Rao said, adding that Parks Department officials had been “innovative partners’’ in helping expand the festival from a smaller venue in Central Park to the Great Lawn.

The Parks Department said OZY Fest met the department’s rules and is hardly unusual for the Great Lawn. Organizers paid $1.5 million to use the venue, officials said.

The festival “joins in a tradition of enriching activations of this public space,” said Crystal Howard, an agency spokesman, and cited other Great Lawn events that, while mostly free, did have a percentage of paid tickets, including shows by the Black Eyed Peas, Andrea Bocelli and Mariah Carey.