The “relentless pursuit” which was “at the hands of a ring of highly aggressive paparazzi” lasted over two hours and resulted in multiple near collisions, they said.
The near collisions were “involving other drivers on the road, pedestrians and two NYPD (New York Police Department) officers,” they added.
“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,” they 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.”
The couple's spokesperson said the chase could have been fatal and involved paparazzi driving on the sidewalk, running red lights, and driving while taking pictures.
The pursuit is understood to have involved six blacked-out vehicles with unidentified people driving recklessly and endangering the convoy and everyone around them.
Pictures that have appeared on social media show Harry, Meghan and her mother Doria Ragland sitting in the back of a New York taxi.
Omid Scobie, a journalist and co-author of Finding Freedom, claimed that the cars continued their pursuit of them despite being confronted by uniformed officers.
“Traffic violations by the drivers include driving on a sidewalk, going through red lights, reversing down a one way street, driving while photographing and illegally blocking a moving vehicle,” he said.
The incident followed Meghan’s attendance at Tuesday night’s Ms Foundation for Women’s 50th anniversary gala event in Manhattan with her husband and Ms Ragland.
The BBC said it was understood Harry and Meghan were staying at a friend’s home in New York and did not return directly after leaving the event at the Ziegfeld Ballroom in midtown Manhattan to avoid compromising their security during the chase.
Police said there had been no injuries or arrests.
Julian Phillips, the deputy commissioner of the New York Police Department, said officers “assisted the private security team protecting the Duke and Duchess of Sussex”.
He continued: “There were numerous photographers that made their transport challenging. The Duke and Duchess of Sussex arrived at their destination and there were no reported collisions, summonses, injuries, or arrests in regard.”
New York Mayor Eric Adams described the actions of the photographers as “reckless and irresponsible”.
He added: “You shouldn’t be speeding anywhere, but this is a densely populated city, and I think all of us, I don’t think there’s many of us who don’t recall how his mom died.
“It’s clear that the paparazzi want to get the right shot, they want to get the right story, but public safety must always be at the forefront.”
The taxi driver who said he picked up Harry and Meghan and her mother said the incident was not a “chase”.
In an interview on Wednesday, taxi driver Sukhcharn Singh said he picked the trio up along with a security guard in New York on Tuesday night and drove them for a brief period.
Singh said he picked them up in his yellow cab at about 11pm outside the New York City Police Department’s 19th precinct on East 67th Street. In Singh’s account, the guard waved him down and asked: “Do you want a fare?”
Singh, who goes by “Sunny,” said he drove the group the block and a half west to Park Avenue before heading south. The driver said they were pursued by two vehicles: a black Honda Accord and an older gray Honda CR-V.
“They kept following us and were coming next to the car,” Singh said. “They took pictures as we stopped and were filming us.”
Singh, 37, said he got the impression from the group that they had been already pursued by paparazzi before entering his car. After a few minutes he said the security guard grew concerned about the photographers and asked him to return to the police station.
The guard thought they were too exposed and didn’t want their location shared more widely, Singh said.
He turned and headed north up Madison Avenue, driving them back to the pickup point. Singh estimated that the entire journey lasted 10 minutes.
He said: “I don’t think I would call it a chase. I never felt like I was in danger. It wasn’t like a car chase in a movie. They were quiet and seemed scared but it’s New York — it’s safe.”
Harry is suing the British government over his security arrangements when in the U.K. Although he travels with his own security, he wants to pay for specially-trained British police officers, who have access to UK intelligence. The British government has resisted setting a precedent where individuals can pay for police.
Meghan accepted a Women of Vision award at the Ms. Foundation Women of Vision Awards: Celebrating Generations of Progress & Power at Ziegfeld Ballroom.
The ceremony was the first public event the Duchess of Sussex attended after the Coronation of King Charles on May 6, which Prince Harry attended without her.
The award honored Meghan’s “lifelong advocacy for women and girls,” including as a United Nations Women’s advocate for women’s political participation and leadership, according to the Ms. Foundation Women of Vision Awards website.
The incident has come amid several High Court trials involving Harry in the UK.
The Duke is attempting to bring a second legal challenge against the Home Office over his security arrangements when in the UK.
He is also bringing a contested claim against Mirror Group Newspapers (MGN) over allegations of unlawful information gathering.
The trial – expected to last up to seven weeks – began last week, with the duke set to appear as a witness in June.
Harry is also one of several seven people, also including David Furnish, Sadie Frost, Liz Hurley and Sir Simon Hughes, bringing legal action against Associated Newspapers Limited over denied allegations it carried out or commissioned unlawful information gathering.
The allegations include hiring private investigators to place listening devices inside cars, “blagging” private records and accessing and recording private phone conversations.
ANL, which “firmly” denies the allegations, asked a judge to rule in its favour without a trial, arguing the legal challenges against it were brought “far too late”.
Prince Harry’s mother, Princess Diana, was killed in a 1997 car crash in Paris while being chased by photographers.