LOS ANGELES — Television executives always say the same thing about remakes: We recycle shows only when we have strong, fresh ideas for them.

It’s almost never true, of course. Remakes like the recently canceled “Muppets” and the much-maligned “Fuller House” usually materialize because dusting off old hits carries less risk than trying to introduce new ones.

But a few rare “reboots,” to use the Hollywood term, do put storytelling concerns ahead of business needs, or at least beside them, and the reimagined “24,” which Fox is to unveil to advertisers on Monday, appears to be one of them. Built by the same team of producers who turned the original series into a cultural touchstone — in many ways, “24” ushered in the era of binge viewing — “24: Legacy” will arrive in early 2017, with a debut after the Super Bowl.

“We understand the skepticism, but there was no corporate mandate here,” said Howard Gordon, a returning executive producer. “If anything, it was the opposite. When we started discussing ideas a year and a half ago, the message was to be slow and careful, to only proceed if the creative team felt it had something that fans would love.”