Amid a rash of cop suicides that had the mayor making a personal appeal to every cop in the city, the police commissioner announced a new game plan to address the crisis.

The department announced three new initiatives to combat the scourge.

The first is set to roll out in a matter of days. A new app will launch on cops’ department-issued smartphones, putting access to emergency mental health services at their fingertips, the NYPD said.

“Press on that app and it’ll give you everything you need to know: where help is and, most importantly, what the signs of suicide are,” NYPD Commissioner James O’Neill told 1010 WINS radio, adding that it will allow easy access to groups including the American Foundation for Suicide Prevention.

“I urge every member of the department, when it appears on your phone, take a look at it,” said O’Neill of the app, which The Post previously ­reported was in the pipeline. “It gives you everything you need to know. It’s about issues you might be having or issues your partner or friends or ­co-workers may be having.”

The NYPD also is working on expanding health insurance coverage for its cops, to ensure they can connect with mental health experts on their own time, should they prefer that to on-the-job counseling.

“We’re expanding the health coverage network for providers that are within network for police officers so they can use their private insurance,” O’Neill said.

In the third initiative, the NYPD is partnering with a city medical facility, which cops can contact around the clock to receive an in-person counseling appointment or FaceTime video call within 24 hours.

“It’s anonymous,” O’Neill said of the medical help. “It’s a road to being healthy and well again, and it’s a road to get you back to what you came on this job for.”