John Key told reporters in India today that the post was inappropriate. He had spoken to his son and he said he recognised that as well.
"He's rung me to both explain and apologise," he said.
"Clearly he didn't mean to make the sort of comment that he made in the way he did, but he fully takes responsibility for it.
"I've told him it it's not appropriate, he's apologised and assured me he won't do it again."
John Key is in India with wife Bronagh and a business delegation including cricketing superstar Brendon McCullum, and met with Indian Prime Minister Narendra Modi today.
The Prime Minister said he didn't know if his son filmed the video or was driving the car.
He said it was a "poor attempt at humour".
The Herald spoke to Max Key who said he had no comment to make. He has since deleted the video.
Cycling Action Network said the video was cringe-worthy, but acknowledged it was not the worst behaviour cyclists have come across.
CAN spokesman Patrick Morgan said: "It makes you cringe because it's wrong on so many levels.
"It's not funny or original, it's vaguely homophobic and I think Donald Trump would be proud - but I suspect everybody else will be rolling their eyes.''
Morgan said the kind of behaviour cyclists faced included drivers being annoying, bullying and physical assault.
"It's by no means the worst that we've seen.
"It's not really a story about cycling. It's just a story about someone being a dick, really.''
Despite Key's choice of words towards the group, Morgan praised him for keeping his distance.
"It appears he's passing with well over a metre to spare.''
A police spokeswoman said it was unclear whether Key was driving the car as he shot the video, but warned people of the dangers of using a cell phone while driving.
"While it is an infringement to use a mobile phone while driving, it is unclear from the very brief video footage whether the person using the phone is also driving.
"However, police would have concerns about any member of the public who chose to drive and film, text or use their phone at the same time - which is why we continue to encourage all drivers to remove distractions such as mobile phones to keep everyone safe on the road.''