Ms. Bagby’s email said a former student had also been involved in the video, which she said had been shot “a few years ago.” It surfaced amid a dispute between the students, according to a person who had been briefed on the situation but spoke on condition of anonymity. The story was first reported by The Daily News, which posted the video on its website.

The video injected Fieldston into the national conversation about racism a little more than a month after a blackface video went viral at another private school in New York, Poly Prep Country Day School in Brooklyn. That incident propelled New York City’s private schools, which are overwhelmingly wealthy and white, into an often-painful dialogue as the city struggles to integrate its public schools and issues like income inequality and the concentration of wealth have increasingly figured in the political discussion.

Fieldston, with a tuition of $52,993 this academic year, according to its website, said that nonwhite students make up nearly 40 percent of its 1,500-person student body, from prekindergarten through 12th grade. Fieldston said it grants more than $14 million a year in financial aid.

Once school officials learned of the video, the school acted rapidly. Ms. Bagby’s email on Monday was the second about the video in two weeks. The first — from Ms. Bagby and the principal of the upper school, Nigel D. Furlonge — was sent on Feb. 13.

“The anguish and outrage so many of us feel cannot be overstated enough,” it said. “We have a strict no-tolerance policy when it comes to acts of bias and hate speech.”