New York City officials have vowed to swiftly find and prosecute any and all hate-crime suspects after a man threatened to kill an off-duty policewoman wearing a traditional Muslim head scarf.

"If anybody's thinking in New York City about engaging in this type of behaviour, just rest assured that you will be identified, you will be arrested, you will be charged accordingly," Police Commissioner James O'Neill told reporters.

Officer Aml Elsokary, a native New Yorker and Muslim, was walking with her teenage son on Saturday in Brooklyn's Bay Ridge neighbourhood, when a man lunged at the boy, accused the pair of being connected to the militant Islamic State group and threatened to cut Elsokary's throat, police said.

The suspect was heard yelling, "Go back to your country," before fleeing, police said.

Christopher Nelson was arraigned on Monday on a top count of felony menacing in the second degree as a hate crime, the Kings County District Attorney's office said.

Civil rights groups have voiced alarm over a rise of attacks on minorities since Republican Donald Trump's Nov. 8 election as president.

New York police said crimes targeting Jews, Muslims, gays and other groups had jumped to 43 since the election compared to 20 during the same period last year. More than half the new attacks were anti-Semitic, police said.

Elsokary, with the force for 11 years, is among 900 Muslims on the country's largest police department. In 2014, she was honoured for rescuing a young girl and her grandmother from a burning building.

"I became a police officer to show a positive side of a New Yorker Muslim woman," Elsokary told reporters. "I'm born and raised here, and I'm here to protect you."

Mayor Bill De Blasio, a Democrat, told the news conference he believed the spike in reported hate crimes was a result of Trump's win, adding, "We could lose lives because of this."

"I was sick to my stomach when I heard that one of our officers was subjected to threats and taunting simply because of her faith," the mayor said. "We must not allow this kind of hatred and bias to spread."

During the campaign, Trump pledged to build a wall along the U.S.-Mexico border and to deport millions of illegal immigrants. He weighed restricting Muslim immigration. Since his victory, Trump has said he rejects acts of violence or harassment.

The Federal Bureau of Investigation describes a hate crime as a "criminal offence against a person or property motivated in whole or in part by an offender's bias against a race, religion, disability, sexual orientation, ethnicity, gender, or gender identity."

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