Decorated NYPD Officer Brian Moore died Monday with his stricken family at his hospital bedside — leaving an entire city awash in grief.

President Obama, speaking at Lehman College, declared “New York’s Finest lost one of its own today,” and that Moore came from a family of police officers who “deserve our gratitude and our prayers not just today but every day. They’ve got a tough job.”

“Policing is never easy,” NYPD Commissioner Bill Bratton said Monday evening. “At this time in America, it’s even more difficult … I’ve been doing this for almost 50 years, and it never gets easier, and I’ve heard this at almost every police death, ‘Why is it always the good ones?’ Maybe the reason it’s always the good ones is because there are so many good ones.”

He announced that Queens prosecutors will put the case before a grand jury Tuesday and upgrade charges to first-degree murder of a police officer.

Investigators found the gun used in Moore’s shooting. They are doing ballistics tests on the five-shot Taurus Model 85 revolver, which has a 2-inch barrel and was found hidden under a box, beside a backyard BBQ next door to where Demetrius Blackwell was arrested Saturday night.

The gun, which still held two live rounds, was stolen on Oct. 3, 2011, one of 23 guns stolen at a bait and tackle shop in Perry, Ga. Nine of those guns have since found their way to New York streets.

A grim-faced Bratton was seen entering Jamaica Hospital as news of Moore’s death Monday afternoon surfaced, and around the same time, two cops also went in — one carrying a pair of shiny shoes and the other a police dress uniform.

Bratton later hailed Moore — who was shot in the head in the line of duty in Queens on Saturday — as one of many cops who “do a great job, often with great valor.

“It’s with great regret and sadness that we announce the passing of New York City Police Officer Brian Moore. Shield number 469. New York City police officer, hero of the city, killed in the line of duty,’’ Bratton told reporters outside the hospital.

“In his very brief career, less than five years, he had already proven himself to be an exceptional young officer,’’ Bratton said. “In that career, he had made over 150 arrests, protecting and serving the citizens of this city.

“He had already received two exceptional police service medals and two meritorious police service medals. We don’t give them out easily.”

Police union chief Pat Lynch said that “now, we are going to take part in a sad, sad tradition’’ — carrying a cop’s casket out of a hospital.

Moore’s body taken from the hospital in an ESU truck as hundreds of cops stood outside and saluted.

A weeping woman believed to be a relative reached out and tried to touch the truck, while a crying man, also appearing to be family, saluted.

The truck was accompanied by a full police escort to the morgue at First Avenue and 28th Street in Manhattan, where an autopsy will be conducted, sources said.

Lynch said that while the entire force is in mourning, cops will still be hitting the beat to keep the city’s streets safe.

“They may have sadness in their eyes, but they have bravery in their hearts,’’ he said of the officers.

There had been little hope for Moore since he was shot in the forehead, with the bullet exiting the back of his neck, tearing through his brain stem, sources said.

During emergency surgery, Moore had to have half his brain removed, so even if he had survived, he would have been completely incapacitated, sources said.

Moore’s dad, retired NYPD Sgt. Raymond Moore, “is devastated,” a source said.

Grieving neighbors began putting up blue bunting on their own houses and NYPD blue ribbons on their mailboxes along the street after learning of Moore’s death.

Blackwell is accused of gunning down Moore after the cop and his partner stopped him because he was suspiciously fidgeting with something in his waistband.

“Do you have something in your waist?’’ Moore asked Blackwell, 35, while sitting behind the wheel of the cops’ unmarked car, sources said.

“Yeah, I got something,” Blackwell snarled back.

Blackwell then whipped out a handgun and fired at the cops three times, sources said.

Moore was hit at least once. His partner, Erik Jansen, was not struck. Two bullets have been recovered from the scene, sources said.

As the city prepared for its third cop funeral in five months, more tributes for the dead officer poured in.

“Our hearts are heavy today as we mourn the loss of Police Officer Brian Moore,” Mayor Bill de Blasio said in a statement.

“For five years, Brian served with distinction and he put his life on the line each day to keep us all safe. On Saturday, he made the ultimate sacrifice in service to the people of New York City.”

Gov. Andrew Cuomo said in a statement, “The shooting of Officer Brian Moore over the weekend was a deplorable act of violence that has robbed New York of one of its finest. As a member of the NYPD, Officer Moore put the safety of his fellow New Yorkers before his own, and we will remember his service with gratitude and pride. I join with all New Yorkers in mourning his passing and send my deepest condolences to his friends and family.”

Additional reporting by Lorena Mongelli, Kevin Sheehan, Sarah Trefethen, Reuven Fenton, Geoff Earle, Yoav Gonen and Kate Sheehy