"Some people will make the case I should be the censor, but on the other side of the coin I'm Prime Minister, but I'm also a father. Most fathers let their kids have social media pages," he said.
"I've wanted my kids to grow up naturally as much as they can, to run their own lives.
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"They've got to take the good and the bad that comes with that. And there will be plenty of bad that comes along and there will be plenty of good as well."
Asked about the video, United Future leader Peter Dunne said politicians' children should generally be off-limits, "after all they do not choose their parents' career or lifestyle".
"Max Key is an adult responsible for his own actions. His parents are not responsible for him, nor is he responsible for them. You have to trust your adult children to make the right decisions, and live their own lives."
Green Party co-leader James Shaw said his only comment was that politicians' children were out of bounds: "It is not their fault that their parents are politicians".
Act Party leader David Seymour said he had not seen the video, "but from what I can gather he hasn't harmed anybody".
"And, frankly, what annoys me about it is the tall poppy syndrome that they see a kid out having fun, and the idea is that the Prime Minister should be asked to say, no, don't do that and show off.
"Everything I hear is that he is a well-mannered young man and he has had his dad busy as hell as the PM for basically his entire teenage years, and people should leave him alone."
Labour leader Andrew Little said the Prime Minister was elected, not his son.
"I have no comment to make about what Mr Key's family members do."
