"It brings up trust issues, which have probably existed between parents and children for years anyway.
"Parents want to be involved in what their children are up to because they love them and want to protect them,'' he said.
But NetSafe executive director Martin Cocker warned that the world parents stepped into online might shock them.
"We find when parents do venture into the teenage world they read a whole lot of stuff which shocks them, which in the context of the teenage world, isn't shocking.
"So sometimes you're best to just stay out and look for more important symptoms of whether your child is happy and comfortable, not to go in and see what they're saying to others online.''
He did point out parents had the right to check their children's Facebook though.
"I don't think that parents would have been outside of their rights as a parent ... it's in an interesting legal space as to how much privacy any individual should have from another individual ... the child/parent relationship tends to be exempted from those privacy arguments.''
The problem was that if parents did find something on their child's page which they were unhappy with, they would then have to admit they had snooped, breaking any trust, Mr Cocker said.
Kiwifamilies.co.nz editor Rochelle Gribble said it was easy for teenagers to get themselves into trouble, and checking on children's internet use was a responsible parent thing to do.
"They probably won't like that, but like everything, we actually have the right to put some parameters around the things they do.''
She admitted that - while her children were aged only one and three at the moment - she intended to snoop on their internet activities when they were older.
But she added, it was an issue that should be discussed with children from a young age.
"I guess it's like the whole sex talk kind of thing - you don't actually want to be talking about it for the first time if you suspect that your child might be doing the naughty, you want to start talking about it when they understand what you're talking about, and so you plant those seeds about it before it's actually a reality for them,'' Ms Gribble said.
The AVG study also found 26 per cent of parents had seen explicit or abusive messages on their teenager's social network profile.
Of the New Zealand parents surveyed 17 per cent suspected their child was "sexting'' - a figure which Mr Cocker said "83 per cent of New Zealand parents need to wake up [to]''.
Twenty-seven per cent of New Zealand parents suspected their teenager of illegally downloading music.
Over half of New Zealand parents (60 per cent) were connected with their teenagers on Facebook.
An Auckland mother of a 16-year-old said she did not have a problem with keeping an eye on what her son was doing or saying on Facebook.
"I think of it like this, employers can potentially see anything your kid writes. At 16 they're usually too stupid to think about that. Even if their Facebook walls are private, they are often friends with adults who might be friends with the employer. It's up to me to say to my son `Hey do you really think you should be making jokes about people or trolling like that?'
"Sometimes he has a rethink, other times he says `I'm gonna cut you off as a friend'.
"I say `Good luck getting your own internet access then' - he hasn't done it yet.''
The boy's grandmother was on Facebook too, so the mother did not want her to be too shocked by what he was saying.
"I don't interfere or comment on stuff that is just usual boy bravado and crassness, that's just how boys are and if he wasn't writing it he would be saying it.
"But I do draw the line at any comments that might be perceived as potential bullying. The problem comes when he answers with `Na you don't understand, that's just how me and so and so are and talk to each other'. There's no way of knowing if that's true so you just have to trust that it is.''
The thing that annoyed him most was if she occasionally wrote something funny as a comment on his status update and it got more likes than his status update.
Plenty of Facebook users today took to the website to discuss whether they thought it was appropriate to access other people's Facebook accounts.
MizLiz Takamore said: "Check their pages regularly I say ... Kids are only entitled to privacy rights when they are earning for themselves and living under their own roof. While they're still minors I and the rest of our whanau are responsible for them ...''
Rob Hawker was succinct in his message: "Below 16 absolutely. Above 16 only with their permission.''
Dave Roberts: "Of course it's OK. Teenagers have no sense of responsibility with social networking, no sense of holding back. They need to be carefully monitored until they can be trusted to act responsibly ... These is a new phenomenon that even adults are not sure how to use properly _ how can we then expect our children to do the same?''
Helen Wood added: "It's rather tragic that anyone would need to betray their child's trust like that. If you're a good parent, you don't need to be sneaky, just try talking to your kids.'
