Three NYPD officers made a daring rescue of an armed man who tried to jump from a seventh-floor window during a routine call to a Harlem housing project.

Officer Vincent Gagliostro, and his partner Isaias Alica knocked on the door of a two-bedroom apartment around 8:30 a.m., Thursday after a tipster said they suspected child abuse or neglect and drug dealing inside.

A woman answered the door and allowed the cops in after a brief hesitation, police said.

The cops said before they could search the second bedroom, a Michael Mulraine, 40, slammed the door and locked it.

The cops convinced Mulraine to open the door so they could make sure no children were injured, but he allegedly flung himself on the bed with his hand under a mattress, where cops say they could see part of a gun.

“I could see the handle of a firearm in between the mattresses,” Alica said. “I struck up a conversation, trying to make him a little more comfortable. I tried to make it seem like I didn’t see the firearm.”

When the suspect allegedly got up from the bed, without the gun, and tried to flee, cops said they grabbed the gun.

Mulraine tried to run but was cornered and went for one of the cop’s collapsible nightsticks, police said.

“I didn’t let him get it,” Officer Alica said. “He pushed me back. He pushed my partner back and tried to jump out the window.”

Alica and his partner, Gagliostro, were close behind and grabbed the distraught suspect’s arm and leg.

“He was out,” Alica said. “He was screaming ‘let me go! Let me go! I want to die!”

With help from a third cop, Kamal McAllister, who arrived after a call for backup, the duo pulled Mulraine to safety then cuffed him and charged him with assault, criminal possession of a weapon and resisting arrest.

No children were found inside and the gun was not loaded but an 11-month-old lives in the apartment, police said.