The FBI will now oversee the investigation of this week's attack on a New Jersey kosher grocery store, which officials are treating as an act of domestic terrorism, federal and state law enforcement officials said on Thursday.

Six people — including the man and woman who carried out the attack, three civilians and a police officer — died in a series of events that ended in a police shootout on Tuesday in Jersey City, N.J., across the Hudson River from New York City.

"The evidence points towards acts of hate," state Attorney General Gurbir Grewal told a news conference. "I can confirm that we are investigating this matter as potential acts of domestic terror, fuelled both by anti-Semitism and anti-law enforcement beliefs."

New Jersey U.S. Attorney Craig Carpenito told the same news conference that the FBI would lead the probe.

The four-hour gun battle at the JC Kosher Supermarket erupted after the pair shot the police officer at a nearby cemetery and then fled in a white van. It ended after police crashed an armoured vehicle through the wall of the market.

Authorities said they were examining social media posts and other evidence to learn more about the attackers' motives. At least one of them appeared to be linked to a group called the Black Hebrew Israelites, a group unaffiliated with mainstream Judaism; some of the offshoots of the group are listed by the U.S.-based Southern Poverty Law Center as hate groups.

Authorities have not established an official link between the shooters and the group, Grewal said. The attackers appear to have acted alone, officials said.

Officials on Wednesday identified the shooters as David Anderson, 47, and Francine Graham, 50. The three civilian victims inside the market were Mindel Ferencz, 32, Douglas Miguel Rodriguez, 49, and Moshe Deutsch, 24, they said.

A fourth person who was in the market escaped after the shooters entered. Officials declined to identify that person.

The slain police officer was identified as Joseph Seals, a 15-year veteran of the Jersey City Police and father of five.

Jersey City Mayor Steven Fulop has called the incident a hate crime since hours after the attack.

"I think as more info comes out it will be more and more clear not only that this was a hate crime but that the perpetrators had hoped to kill many more people than [four]," Fulop said earlier on Twitter.