The rookie cop who killed an armed 14-year-old thug with a single shot in The Bronx Sunday was remarkably restrained given the danger of the situation, the head of the city’s police union said yesterday.

The unidentified cop and his partner had heard gunfire and confronted suspected gang member Shaaliver Douse, 14, as the youth fired bullets at a rival in the Melrose section.

“These officers were put in the extremely difficult situation of encountering an armed individual who was firing his weapon,” PBA President Patrick Lynch said.

Douse’s mom, Shanise Farrar, said of her son, “I’m not saying that he’s the best one, but he’s my angel.”

Meanwhile, authorities said they have traced the gun Douse was firing back to a Kentucky sporting goods store. Investigators are trying to find the gun’s original owner and determine how it ended up in New York.