"We all make mistakes when we were young – I would think it's part of the growing up process," Peters said.
But he did quip that "by the looks of it, he's still growing up".
The photo, which has been reported on by media since surfacing online, shows Wood posing like Hitler with what appears to be a painted on small moustache.
It appears to be a photo he sent to a friend – or group of friends – which appears to have been leaked.
Wood, now aged 18, told TVNZ the photo was an error and has apologised.
He said he was 14 when it was taken.
"I apologise for any offence I may have caused."
Seymour said he wouldn't be punishing someone for something they did when they were 14 – "I would just tell them it was something that was very bad taste."
"I certainly hope that, if he is now mature enough to be a candidate he understands it's the wrong thing to do."
But he said that frankly, "going after someone for something they did when they were 14, no matter how stupid, I don't think helps New Zealand solve its problems."
Seymour and Peters have been at each other's throats over the last couple of weeks over a number of issues.
It started off fairly bloodless, having cracks at each other on Twitter about having fistfights.
"There'd be three hits - you hitting me, me hitting you, and the ambulance hitting 100. Thank your lucky stars I'm not into physical violence," Peters Tweeted.
This was in response to comments about his age from Seymour.
But last week, the beef took a more serious turn after Peters claimed in the House Seymour was involved of the leaking of his superannuation information in 2017.
Speaking to reporters, Seymour denied this.