The incident involved "a ring of highly aggressive paparazzi" in half a dozen cars with blacked out windows, driving dangerously and putting the lives of the couple and Doria Ragland in danger.
"This relentless pursuit, lasting over two hours, resulted in multiple near collisions involving other drivers on the road, pedestrians and two NYPD [New York Police Department] officers," the spokesperson said in a statement.
The couple - the Duke and Duchess of Sussex - were shaken by the incident but otherwise unharmed.
The New York Police Department said it had assisted the private security team protecting them.
"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," an NYPD spokesperson said.
The Washington Post quoted taxi driver Sukhcharn Singh, who said he drove the group and a security guard for around 10 minutes before returning to the police station he had picked them up from at the security guard's request.
"I don’t think I would call it a chase," Singh was quoted as saying, adding that two vehicles had followed them and come next to the car, taking pictures and filming.
"I never felt like I was in danger. It wasn’t like a car chase in a movie. They [the couple] were quiet and seemed scared but it's New York — it's safe."
Pictures on social media show Harry, Meghan and her mother sitting in the back of a New York taxi which their spokesperson said showed "a small glimpse at the defence and decoys required to end the harassment".
Media reported the couple had switched to the taxi to try to shake off the photographers, after the car they left the Ziegfeld Ballroom in midtown Manhattan in was pursued.
"HIGHLY INTRUSIVE"
The prince has long spoken out about his anger at press intrusion which he blames for the death of his mother Princess Diana, who was killed when her limousine crashed as it sped away from chasing paparazzi in Paris in 1997.
The couple's spokesperson said the chase on Tuesday could also have been fatal and involved paparazzi driving on the sidewalk, running red lights, and driving while taking pictures.
Those involved were confronted by police officers multiple times, according to the spokesperson.
New York City Mayor Eric Adams said he had received a briefing that two NYPD officers could have been injured in the incident.
"I don't think there's many of us who don't recall how, how his mom died," Adams told reporters. "And it would be horrific to lose an innocent bystander during a chase like this and something to have happened to them as well."
He said he would be given an in-depth briefing later, but that he found it hard to believe there would have been a two-hour high speed chase.
"If it's 10 minutes, a 10-minute chase is extremely dangerous in New York City," Adams said.
The Ms Foundation for Women, the organisers of the awards ceremony where Meghan was honoured for her work, had no immediate comment. Buckingham Palace also had no comment.
The couple, who live in California with their two young children, had been staying at a private residence but decided against returning there as they did not wish to compromise their host's safety, according to their spokesperson.
Harry has never hidden his dislike for the press, fuelled by the treatment his mother received and by his own experiences, particularly when he was young.
In his memoir "Spare", the couple's Netflix documentary series and TV interviews, he has railed against British tabloid newspapers invading his and his family's privacy - one of the main reasons he and Meghan gave for stepping down from their royal roles in 2020 and moving to the United States.
The prince is currently involved in numerous court cases in London where he has accused newspapers of using unlawful methods to target him and his family. While papers reject nearly all his allegations, one publisher last week apologised for unlawfully seeking information about him in 2004.
He is also seeking to overturn a decision by the British government to take away his specialist police protection when he is in Britain.
(Reporting by Michael Holden, William James and Kylie MacLellan in London and Jonathan Allen in New York; Editing by Alex Richardson, Toby Chopra, Daniel Wallis and John Stonestreet.)