This article is more than
5 year oldThe FBI is now overseeing the investigation into the attack in Jersey City, where four people were killed.
Police shot two suspected attackers after a four-hour standoff.
The suspects were identified as David Anderson, 47, and Francine Graham, 50.
"The evidence points towards acts of hate," state Attorney General Gurbir Grewal said.
"We are investigating this matter as potential acts of domestic terror, fuelled both by anti-Semitism and anti-law enforcement beliefs."
He said the attackers had only fired on people in the supermarket and police officers.
"You can see clearly from the video that the individuals that engaged, the cowards that took down those innocent victims, engaged only with folks in that store and the law enforcement community," Mr Grewal said.
"You can see people that walked by, they didn't target them."
Mr Grewal said a pipe bomb had been recovered from the suspects' van, which had been equipped with bulletproof panels, along with five guns.
Investigators had found a note at the scene, he added, but nothing that could be described as a manifesto had been found. Officials believe the suspects acted alone.
US media have reported that one of the suspects had made anti-Semitic and anti-police social media posts online before the attack.
At least one of the suspects appeared to be interested in a group called the Black Hebrew Israelites, whose believers say they are the true descendents of ancient Israelites, officials said. The group is listed by the Southern Poverty Law Center as a hate group.
But Mr Grewal said no official link with the group had been established.
Earlier Jersey City Mayor Steven Fulop tweeted that "hate and anti-Semitism" had no place in the city.
"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," he said.
The violence began at a cemetery about one mile (1.6km) away from the grocery store.
The pair killed Detective Joseph Seals, 39, who approached them for questioning about the murder of an Uber driver over the weekend, investigators said.
Thy fled the scene in the van and drove to the kosher supermarket at 12:20 local time (17:20 GMT) where they held off armed police and federal officials for four hours, shooting off hundreds of rounds of ammunition.
The attackers had opened fire on the shop before entering, alerting two officers on foot patrol who began firing at the suspects until they were injured by the attackers' gunfire.
Mr Fulop told reporters that street cameras showed two people "slowly" drive towards the market, then "calmly open the door with two long rifles and begin firing from the street" into the shop.
The incident ended just before 16:00 when officials used an armoured vehicle to ram through the front entrance of the shop and found the bodies of the attackers.
The attack put approximately 30,000 students on lockdown, unable to leave their classrooms for hours after the school day had ended.
The three victims inside the shop were killed soon after the gunfire broke out, but one managed to escape after being injured.
They have been identified by New Jersey officials as Mindy Ferencz, 32; Miguel Douglas, 49; and Moshe Deutch, 24.
"Mindel Ferencz, may she rest in peace, was a pioneer," said Rabbi David Niederman, who first confirmed the death of the mother of five.
"She was a lady full of love for others," he added. "Unfortunately, her life was cut so short."
Ferencz's mother told the New York Times that her husband, who owned the supermarket, had taken a break from work to go to a nearby synagogue minutes before shots rang out.
Deutsch's death was also confirmed by Rabbi Niederman, who hailed him as a student who had worked to organise a food drive that provided help to 2,000 families each year.
New York City Mayor Bill de Blasio called the attack a "hate crime" and an "act of terror", and ordered police to be on high alert, especially in Jewish communities. Jersey City is part of the New York metropolitan area.
"This confirms a sad truth. There is a crisis of anti-Semitism gripping this nation. There is a crisis of anti-Semitism in this city," he said in a Wednesday news conference.
He added: "History tells us to take these warning signs seriously."
New York Police Department commissioner Dermot Shea added that hate crimes in New York City were up 22% this year.
"You see a swastika being drawn, you see a brick being thrown through a window, you see a woman walking down the street with her kids and having her wig ripped off," he said.
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