The Sussexes allege the chase involved half a dozen cars driving dangerously including by going through red lights, driving on the pavement, carrying out blocking moves, and reversing down a one-way street - as well as taking photographs while driving.
The trio then hid from the paparazzi by going to a Manhattan police station before flagging down a New York Taxi. But photographers saw them so they returned to their own security vehicle.
What did the couple say?
Here is their spokesperson's statement in full:
"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 that 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.”
“Dissemination of these images, given the ways in which they were obtained, encourages a highly intrusive practice that is dangerous to all involved.”
Cab driver Sukhcharn Singh, who goes by the name Sonny, told BBC News he picked up the four passengers on 67th Street between Lexington Avenue and 3rd Avenue.
"A security guard hailed me, next thing you know Prince Harry and his wife were hopping into my cab," he said.
"As we went a block, we got blocked by a garbage truck and all of a sudden paparazzi came and started taking pictures. They were just about to give me the location of where they were going to go, but then they told me to circle back to the precinct."
He said they were "nice people" who "looked nervous".
He thought claims of a "near catastrophic chase" might have been exaggerated, saying that he did not think the paparazzi were being "aggressive".
"New York is the safest place to be - there's police stations, cops on every corner," he said.
"[The paparazzi] were behind us... they kept their distance."
Speaking to CNN, he added that when the couple got in his car “all of a sudden the paparazzi just stormed the taxi. There’s flashes coming from every direction. They’re up against the car, taking pictures.”
At one point, Singh said, a security guard in the cab with them got out to tell the paparazzi to move.
Singh said that he didn’t personally feel in danger but the Duke and the Duchess appeared “very nervous.”
“The look on their faces, you could tell that they were nervous and scared,” Singh recalled.
What have security said?
Chris Sanchez, a member of the couple's security detail, told CNN the scene was "very chaotic" and that photographers at one point blocked the limousine carrying Harry and Meghan.
"The public were in jeopardy at several points," he said. "It could have been fatal."
\u201cExclusive: Member of Prince Harry and Meghan's security detail tells @MaxFosterCNN there were about a dozen vehicles pursuing the couple after last night's event in NYC. \n\n"The public were in jeopardy at several points. It could have been fatal."\u201d
— CNN International PR (@CNN International PR)
What have the police said?
The New York Police Department (NYPD) said there were no arrests or injuries. But they confirmed an incident took place involving Harry and Meghan and said numerous photographers "made their transport challenging".
What have the paparazzi said?
Entertainment picture agency Backgrid issued a statement saying it was investigating the conduct of several freelance photographers, but said: "the photographers have reported feeling that the couple was not in immediate danger at any point."
A paparazzi driver reportedly involved in the allegedly high-speed New York car chase of the Duke and Duchess of Sussex has said that it was “very tense” trying to keep up with their vehicle.
Speaking anonymously to ITV’s Good Morning Britain on Thursday, the driver said: “Last night after leaving the theatre, there were hopes from me and a few other photographers that maybe they would go to a restaurant.
“For the most part, I was driving and it was very tense trying to keep up with the vehicles. They did a lot of blocking and there was a lot of different type of manoeuvres to stop what was happening.”
He claimed that Harry and Meghan’s driver made the pursuit “a catastrophic experience”.
“Their driver was making it a catastrophic experience... if they were going 80mph, I would probably have been going 20mph behind them and hoping to keep sight of them,” he said.
“So if it was dangerous and catastrophic, it was more than likely based on the person that was driving.”
What have other royals said?
The Duke and Duchess of Sussex have not been contacted by the royal family after claiming to have been involved in a “near-catastrophic” car chase, the PA news agency understands.
A Buckingham Palace spokeswoman declined to comment.
How have other people reacted?
The mayor of New York City, Eric Adams said the incident was “reckless” and “irresponsible.”
“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,” Adams told reporters when asked about the incident at an unrelated briefing.
“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,” Adams said.
Why were the couple in New York?
The Duchess of Sussex was in New York to accept the Women of Vision Award during the Ms. Foundation’s 50th-anniversary gala at the Ziegfeld Ballroom.
Markle, who was one of four honorees, received the award “for her global advocacy to empower and advocate on behalf of women and girls,” according to the foundation’s website.
Have your say in our news democracy. Click the upvote icon at the top of the page to help raise this article through the indy100 rankings.