Sukhcharn Singh, who goes by the name Sonny, told the BBC he picked them up at a local police precinct in Midtown Manhattan.

Harry and Meghan's spokesperson has said in a statement that the couple endured a "relentless pursuit" that lasted for more than two hours.

But Mr Singh, who witnessed one part of the drama, did not characterise his drive as a dangerous chase by paparazzi.

Dressed in a navy blue shirt and speaking to reporters outside his family's home in Queens, Mr Singh described the headline-making drive.

"I was on 67th Street and then the security guard hailed me. Next thing you know, Prince Harry and his wife were hopping into my cab," he said.

"We got blocked by a garbage truck, and all of a sudden paparazzi came and started taking pictures." Harry and Meghan were about to share their destination when the security guard made the call to return to the police precinct.

"They looked nervous, I think they were being chased the whole day or something," Mr Singh said. "They were pretty nervous, but the security guard, he was on it."

In a statement, Harry and Meghan's spokesperson said they had experienced a "near-catastrophic car chase" on Tuesday. New York police confirmed an incident and said numerous photographers "made their transport challenging" - but that there were no reported collisions or injuries.

One of the paparazzi drivers reportedly involved in the car chase has said it was "very tense" trying to keep up with their vehicle.

Speaking anonymously to ITV's Good Morning Britain on Thursday, the driver said: "They did a lot of blocking and there was a lot of different types of manoeuvres to stop what was happening."

He added: "If it was dangerous and catastrophic, it was more than likely based on the person that was driving."

Photo agency Backgrid USA said it received photos of the event from photographers, "three of whom were in cars and one of whom was riding a bicycle".

The agency said it took Prince Harry's allegations seriously and would be conducting its own investigation, but that according to the photographers, "there were no near-collisions or near-crashes during this incident".

"It is important to note that these photographers have a professional responsibility to cover newsworthy events and personalities, including public figures such as Prince Harry and Meghan Markle," the agency added.

The couple were in New York attending an awards ceremony - the Ms Foundation Women of Vision Awards - along with Meghan's mother, Doria Ragland.

When they were chased after leaving, the spokesperson said, they tried to take shelter from the paparazzi by going to a Manhattan police station - which is where Mr Singh picked them up.

For at least the few minutes they were in Mr Singh's car, he did not believe they were in danger.

"I don't think that's true, I think that's all exaggerated and stuff like that. Don't read too much into that," Mr Singh said of the statement. He later added "that must have happened before" they got in his taxi.

"New York City's the safest place to be," he continued. "There's police stations, cops on every corner, there's no reason to be afraid in New York."

The paparazzi were not being aggressive during his drive, he said.

"They were behind us. I mean, they stayed on top of us, that was pretty much it, it was nothing more. They kept their distance."

Mr Singh described Harry and Meghan as "nice people".

"At the end of the trip, they say, 'Oh nice meeting you'," and asked his name, Mr Singh recalled. As his passengers disembarked, the security guard paid and tipped him for the ride.

"It was great. Ten-minute drive, $50," he said. "What can you ask for? You can't beat that!"

Was Mr Singh dazzled by his famous passengers? Not particularly.

"I have also picked up Keith Richards in my cab as well," Mr Singh said. "I pick up celebrities all the time. I didn't think much of it when they got in, either."

After speaking to reporters for a few minutes, Mr Singh got back in his yellow cab and drove off to Midtown, for another long day of ferrying passengers.