Former Police Commissioner Ray Kelly suggested on Tuesday that the NYPD is manipulating crime statistics — and challenged Mayor de Blasio’s assertion that New York remains the safest big city in America.

When asked during a ­radio interview about data put out by his successor, Bill Bratton, showing overall crime at record lows, Kelly laughed.

“I think you’ve got to . . . look at those numbers because I think there are some issues with the numbers that are being put out,” Kelly said on AM 970. “I think there’s some redefinition going on as to what amounts to a shooting, that sort of thing.

“I mean, look, all administrations want to show that crime is down,” he added.

“But you have to take a hard look at those numbers, and I can tell you, people don’t feel safer in this city. People say this to me all the time. And perception is reality in many instances. So the city feels unsafe in many people’s minds and unsafe in many neighborhoods in people’s minds.”

Bratton and Kelly have challenged each other’s rec­ords, with stop-and-frisk a flashpoint. Reports of such encounters have have plummeted under Bratton, and there has been an ongoing debate over whether severe restrictions on stop-and-frisk have had an impact on crime stats.

Murders are up this year, but shootings are down. Overall, crime is at historic lows, according to NYPD CompStat figures.

The increase in murders comes as a study revealed this month that the NYPD took more than 800,000 fewer “enforcement actions” during de Blasio’s first year in office in 2014 than in Mike Bloomberg’s last year as mayor in 2011 — cutting stop-and-frisks, summonses for quality-of-life violations and misdemeanor arrests.

The John Jay College of Criminal Justice analysis showed that stops made up the majority of the cutbacks, falling from 685,724 in 2011 to 45,787 in 2014 — a 93 percent drop.

“Perhaps Ray Kelly’s looking at the shooting numbers along with the drastic reduction in stop-and-frisks, and his expectation, along with others, [is] that shootings would increase as a result,” a police official said in response to Kelly’s remarks.

“That hasn’t panned out, so now he’s accusing the department of fudging the numbers when the reality is we’re just doing more focused crimefighting.”

The former commissioner has also spoken out about terrorism recently, warning that more bloodbaths like the one in San Bernardino this month are inevitable.

On Sunday, Kelly told John Catsimatidis on AM 970, “We’re going to see more of these [attacks in the United States], unfortunately.

“They’re trying to find some receptive ears to this message and it appears that in San Bernardino, they found that.”

Kelly has fueled speculation of mounting a mayoral run against de Blasio in 2017. The Post reported on Monday that Kelly has given his supporters the go-ahead to contact potential contributors.