Speaking on RadioLive this morning, Mr Whyte admitted he had regretted the comments published in an article on The Ruminator Website.
"I regret the comments, mainly because I feel I let the party down," he said.
The u-turn comes less than a day after he told the Herald he stood by his comments, and his campaign director Richard Prebble called his comments "refreshing" and "frank".
In The Ruminator interview, Dr Whyte - a former philosophy lecturer - was asked whether the state should intervene if adult siblings wanted to marry each other.
"Well personally, I don't think they [the state] should," he replied, adding it was "a matter of almost no significance because it just doesn't happen".
Dr Whyte this morning told RadioLive his comments were out of line with his position as party leader.
"I regret the comment, not because I don't believe it, but because I'm the leader of a political party now. I may have been a philosophy lecturer in the past, but I'm not anymore.
"My personal opinions aren't really relevant anymore."
"Act doesn't have a view on that stuff, and I really shouldn't have been talking about it," Dr Whyte said.
He believed he had been caught in a "gotcha" journalism moment.
"He figured I would fall into my old philosophical ways and draw out the inevitable conclusions in this principal, and I definitely played into his hands.
"He did get me," he told RadioLive.
Dr Whyte yesterday told the Herald his response during The Ruminator interview was based on his belief that "I don't think the state should intervene in consensual adult sex or marriage, but there are two very important elements here - consensual and adult".
"I wonder who does believe the state should intervene in consensual adult acts?"
He said he was "very opposed" to incest.
"I find it very distasteful. I don't know why anybody would do it, but it's a question of principle about whether or not people ought to interfere with actions that do no harm to third parties just because they personally wouldn't do it."
Mr Prebble, a founding member of Act, also said yesterday he didn't see Dr Whyte's comments as a hindrance to his task of building support for the party.
"Actually in some ways it is useful because it shows Jamie Whyte is not a politician and I don't think the public want politicians. Our enemies will attempt to distort that, but I find the guy refreshing and new and I think the electorate is looking for something that's fresh and new.
"He's somebody who's very frank and so when he says things he means it. If you've got a candidate who happens to have been a philosophy lecturer at Cambridge University, you can always ask him 'gotcha' questions."
Dr Whyte was elected Act leader this month but officially takes over from John Banks this weekend.
- By Teuila Fuatai of APNZ and Adam Bennett of the New Zealand Herald
