People board up the front of a kosher supermarket that was the site of the gun battle in Jersey City, N.J.

Bullet holes are seen in a piece of metal at a kosher supermarket, the site of shooting in Jersey City, N.J.

The couple that killed a Jersey City cop then slaughtered three people in a kosher market had even more hateful plans — and a bomb that could have maimed victims up to five football fields away, officials revealed Monday.

But the attackers were forced to retrench when they were confronted by hero police Detective Joseph Seals, leading to his slaying, authorities said.

“We believe he threw off a broader plan,” Newark federal prosecutor Craig Carpenito said at a news conference, adding that Seals “probably saved dozens, if not more, lives.”

Officials said David Anderson and Francine Graham plotted for months before their chance encounter on Dec. 10 with Seals, who apparently spotted their U-Haul van in a cemetery and suspected it was linked to a recent slaying in Bayonne.

After fatally shooting Seals, they headed to the nearby JC Kosher Supermarket, where they killed co-owner Mindel Ferencz, employee Douglas Miguel Rodriguez and customer Moshe Deutsch, then died during a furious firefight with cops.

FBI Special Agent in Charge Greg Ehrie said a homemade bomb found in the couple’s van was powerful enough to cause casualties from as far as 500 yards away.

The van also contained enough material to build a second device, Ehrie said.

Surveillance video shows the couple repeatedly driving by the store in the week leading to the attack — and they also searched the Internet for information about a Jewish community center in Bayonne, officials said during the press conference.

Their anti-Semitism was fueled by beliefs associated with the Black Hebrew Israelite movement, officials said — adding that Anderson used social media to call Jews “imposters who inhabit synagogues of Satan” and “wicked Israelites who love darkness as cover for their wickedness.”

Investigators found at least two notes in Anderson’s pockets, with officials saying one referred to the point in the 1990 documentary “The FBI’s War on Black America” where the late Black Panther leader Fred Hampton denounces “fascist pig cops.”

Video recorded inside the kosher market also shows Anderson saying, “They stole our heritage, they stole our birthright and they hired these guys to stop us,” ­Carpenito said.

The mountain of evidence shows that Anderson and Graham had “planned greater acts of mayhem” on both the Jewish and law-enforcement communities, ­Carpenito said.

DNA testing of Anderson and Graham’s clothing and weapons tied them to the fatal bludgeoning and shooting of livery driver Michael Rumberger, who was found stuffed in the trunk of a Lincoln Town Car in Bayonne on Dec. 7, officials said.

Ballistics testing also tied a gun linked to Anderson with an incident in which the rear window of a vehicle driven by an Orthodox Jewish man was shot out on Dec. 3 as he drove on Routes 1 and 9 near Elizabeth and Newark, officials said. That man was wasn’t injured.