Fred Phillips - a surgeon, former Act New Zealand member and regular blogger - said his children were well behaved and Mr Chauvel's comments were inappropriate.
"It was a petulant act from a public figure who should know better."
Mr Phillips said he heard Mr Chauvel voice his anger three times, culminating at the end of the flight with a comment of "I don't know why they let them up here".
Mr Chauvel disputes this, saying he said to his partner once on the flight that he wished the children would "shut up" and any normal person would have said the same thing.
Mr Phillips' wife, Stephanie, was sitting in the front row with two children, aged 1 and 4, and she did not hear any comments from Mr Chauvel.
But Mr Phillips said the comments were "loud enough for me".
"I was sitting in the row in front of him and I could hear what he was saying very clearly.
"If I hadn't heard anything I wouldn't be upset.
"I was going to ask him to act more maturely, but my wife said it could have escalated into an argument."
He admitted his children were making noise, but nothing of any consequence.
"It was less than the noise being made by the engines of the aeroplane. And they calmed down, it was infrequent and there was no-one else around us who was remotely concerned.
"I am very conscious when I travel with children, and I am the first to try and placate the children if they are being difficult.
"Our children were being absolutely fine. If there is anyone that needs to look at their behaviour or personal management skills, it's not my family."
Mrs Phillips admitted her 1-year-old was difficult for about a minute during the descent, but apart from that the children had not been particularly disruptive.
She was upset at subsequent implications that she was a bad parent.
Mr Chauvel said yesterday he despaired that the incident - which Mr Phillips had blogged about - had become the focus of so much media attention.
"It's a bit frustrating for somebody in my job, who spends half their time trying to get the media to take seriously the fact that we might be in electricity crisis next year, which nobody is interested in.
"And suddenly [the media] getting all worked up about what somebody says on a blog."
He said other passengers on the flight were equally annoyed.
"I recall these kids were being very, very noisy, and turning to the person I was travelling with and just saying, `Gosh I wish they would shut up'.
"It didn't seem they had been given anything to do on the flight except to sit there and screech at each other ...
"I think it was a pretty normal human reaction, actually ... I certainly noticed some people in the aisle opposite me rolling their eyes and at one stage sticking their fingers in their ears, as a joke."
"He said he did not raise his voice, but "clearly, the chap in front of me heard what I said, so maybe I should've been quieter about it".
A person on the same flight came out yesterday in support of Mr Chauvel: "I was on that same flight, and sitting in the aisle across from Charles and I actually said to my husband that I wished the parents would tell their children to `shut up'.
"They were pretty loud."
