Nearly a fifth of parents believe their child has fallen victim to cyber bullying, a survey suggests.
And over half check their child's internet activity at least once a week, according to the poll commissioned by the National Association of Principals and Deputy Principals.
Clive Byrne, director of the association which represents second-level school leaders, said it is critical that parents and carers are vigilant against online bullying.
"While responsibility for dealing with cyber bullying is shared across society, the victim must remain our central focus," Mr Byrne said.
"We must empower our children to use the new tools of the information age while at the same time educate them about the terrible harm they can cause if these tools are abused."
The association will be working with principals to introduce school-wide policies that monitor the risk of cyber bullying, Mr Byrne said.
The survey, by Amarach Research, found that 18% of parents believe their child has been bullied by someone on the internet, although around three-quarters (73%) do not think their son or daughter has fallen victim. Around one in six (12%) suspect that their child has bullied another child over the internet.
Mothers are more likely to monitor their child's internet usage than fathers, at 59% compared with 45%, according to the survey which interviewed 293 parents who have children aged 10-18.
The majority believe schools, parents and victims share responsibility to tackle cyber bullying, although a quarter believe it should be up to the gardai to address the problem.
Last month Children's Minister Frances Fitzgerald published guidelines to help schools deal with cyber bullying.