Police fatally shot a man who stabbed a Jewish student in Brooklyn on Tuesday, officials have confirmed.

Calvin Peters, 49, was captured on video brandishing a knife early on Tuesday morning after having stabbed 22-year-old Levi Rosenblat in the side of the head while he was studying the Torah at the Chabad-Lubavitch headquarters.

A spokesman for Chabad-Lubavitch, Rabbi Chaim Landa, said a witness reported Peters shouting "Kill the Jews!"

Mendy Notik, 22, who witnessed the attack, said Rosenblat "had his hands up, trying to block the individual [Peters] with his arms.

"He [Peters] was saying, 'I will kill you.' And after Levi, he went towards another young student and he said, 'I will kill the Jews!'"

The police were immediately summoned, and ordered Peters to put the knife down. The attacker did so, before picking it up again and lunging at the officers. Officer Roberto Pagan then fired a single, fatal shot.

Rosenblat is in a critical but stable condition.

Police Commissioner Bill Bratton said there is "no indication" that Peters "had any affiliation with any terrorist organisation," but the attack follows an incident in which five people were killed at a Jerusalem synagogue last month.

Two Palestinians used meat cleavers, knives and a handgun in a bloody attack, before themselves being shot dead by police on November 18.

In the wake of yesterday's attack, New York state Assemblyman Dov Hikind said in a statement: "The entire Jewish community is impacted by these cruel and senseless attacks.

"How can we help but be reminded of the recent, horrible tragedy...which left five innocent people dead?" he added, according to the Associated Press.

The NYPD's John Miller told a press conference yesterday that the attack in Brooklyn was an "isolated incident" and noted that Peters had "a history of being an emotionally disturbed person".

"Right now, there's nothing to suggest" that it was a religious hate crime, Chief of Detectives Robert Boyce told reporters.