The incident happened on Tuesday night after Harry and Meghan attended an awards ceremony in New York City.
Meghan's mother Doria Ragland was with them in the vehicle, the spokesperson said in a statement emailed to AFP.
"Last night, The Duke and Duchess of Sussex and Ms. Ragland were involved in a near catastrophic car chase at the hands of a ring of highly aggressive paparazzi."
"This relentless pursuit, lasting over two hours, resulted in multiple near collisions involving other drivers on the road, pedestrians and two NYPD officers," the spokesperson said.
"While being a public figure comes with a level of interest from the public, it should never come at the cost of anyone's safety," the spokesperson added.
The statement said: "Dissemination of these images, given the ways in which they were obtained, encourages a highly intrusive practice that is dangerous to all in involved."
A spokesperson for the New York Police Department did not immediately respond to requests for comment.
Harry, 38, and Meghan, 41 had attended the Ms. Foundation for Women ceremony where Meghan received an award.
The couple quit the royal family in early 2020 and moved from Britain to the United States, in part because of intense media scrutiny.
Harry has long blamed press intrusion for causing the death of his mother, Princess Diana, in a car crash in Paris in 1997 while she was being pursued by paparazzi.
'Diana Deja Vu' For Harry and Meghan
FILE - Britain's Prince Harry, Duke of Sussex, Meghan, Duchess of Sussex attend the 2022 Robert F. Kennedy Human Rights Ripple of Hope Award Gala in New York City, U.S., December 6, 2022.
NEW YORK - Prince Harry and wife Meghan Markle were involved in a "near catastrophic car chase" involving paparazzi in New York, a spokesperson for the couple said Wednesday. A paparazzi chase in Paris in 1997 resulted in a crash that killed Harry's mother, Diana.