A man who authorities said shouted “go back to your country” at a Muslim woman wearing a religious head covering may have picked the wrong target: a decorated New York City police officer.

Officer Aml Elsokary, a New York City native who joined the force after the September 11 attacks, said she was off duty in her Brooklyn neighbourhood Saturday when she encountered a man yelling and pushing her 16-year-old son.

When she intervened, she said, the man referenced the militant Islamic State group and threatened to slit her throat.

It was the first time anything like that had happened to her, she said at a news conference with the city's mayor Monday.

“I became a police officer to show the positive side of a New Yorker, a Muslim woman, that can do the job,” Elsokary said.

“I help everybody, no matter what your religion, what's your faith, what you do in New York. I'm born and raised here.”

The man accused of making the threat, Christopher Nelson, 36, was arraigned Monday on a felony charge of menacing as a hate crime. His attorney did not immediately respond to a request for comment.

The encounter was one of a number of alleged episodes of religious or racial bigotry reported in the city in recent days.

On Monday, a transit worker who is Muslim was pushed down the stairs at Grand Central Terminal by a man who called her a terrorist, police said. The station agent, who was wearing a religious head covering, was attacked while on her way to work. She was treated at a hospital for ankle and knee injuries.

Gov. Andrew Cuomo also noted in a statement that a subway train was vandalised with swastikas on Saturday, and Ku Klux Klan materials were distributed at Long Island Rail Road stations last week.

The police department cited Elsokary for bravery in 2014 after she and a partner ran into a burning building to save a baby. Police Commissioner James O'Neill recalled visiting Elsokary at the hospital where she and her partner were treated for smoke inhalation.

“You and your partner did a tremendous job that day,” O'Neill told her at Monday's news conference. Mayor Bill De Blasio said there are 900 Muslims serving as New York City police officers, on a force of about 36,000.

“In 2014, she ran into a burning building and helped to save a young girl and her grandmother. And, then, on Saturday, she had to experience a man allegedly yelling at her and her son, 'Go back to your country,'” said de Blasio.

“Well this is Officer Elsokary's country. She is an American. She is a New Yorker. She's already at home.”