The government is publishing guidelines to help schools, parents and pupils tackle the issue of "cyber-bullying".
It comes as the Anti-Bullying Alliance publishes research suggesting that up to one in five pupils has been bullied via the Internet or mobile phones.
Schools minister Jim Knight said the Department for Education is to also ask technology firms to help.
Teaching union the NASUWT said teachers were also increasingly being abused via the web, emails and phones.
The guidelines set out simple steps that schools, parents and pupils can take to prevent cyber-bullying and deal with incidents when they occur.
• Schools including strategies to deal with cyber-bullying in their mandatory anti-bullying policies
• All communication technology on the site, or as part of school activities off site, should be monitored and, where necessary, restricted
• Parents should ensure that they and their child understand how to use technology safely
• Young people should not respond to abusive emails, text messages or phone calls, but should always tell an adult and contact their service provider for advice on how to block calls, keeping emails and texts as evidence
• Young people should keep to public areas of chatrooms and never give out personal contact details online or post photographs of themselves
The Anti-Bullying Alliance research identified seven types of cyber-bullying, ranging from abusive text messages, emails and phone calls to bullying in Internet chatrooms, social networking sites and instant messaging.
Up to one in five pupils have experienced some form of cyber-bullying according to the study, which was based on responses from 92 children aged 11-16 from 14 London schools.
Girls were significantly more likely to be subjected to cyber-bullying, especially by text message. However, around a third of victims had never told an adult about the problem.
Mr Knight said: "No child should suffer the misery of bullying, online or offline, and we will support schools in tackling it in cyberspace with the same vigilance as in the playground.
"Every school should account for cyber-bullying in their compulsory anti-bullying policies, and should take firm action where it occurs."
He added that the Education and Inspections Bill would give teachers a legal right to discipline pupils.
Parents of bullies would also face court-imposed parenting orders compelling them to attend parenting classes or face £1,000 fines.
But he warned: "Unlike other forms of bullying, cyber-bullying can follow children and young people into their private spaces and outside school hours.
"This is why it is essential that parents and young people themselves should understand how to use technologies safely to protect themselves at home and outside school hours, as well as supporting their schools in dealing with incidents."
'Climate of silence'
Chairman of the Anti-Bullying Alliance Gill Frances added: "As our research shows, a third of those who experience cyber-bullying do not report it.
"If we are to succeed in preventing bullying, we need to break the climate of silence in which it thrives by empowering children and young people to speak out and seek help."
The NASUWT called for the guidelines to be incorporated into school discipline policies to protect staff.
Its general secretary, Chris Keates, said: "In the last two years we have had cases of photographs of a teacher being superimposed on obscene images on the Internet, a website established to run a hate campaign against a teacher, persistent offensive phone calls to a member of staff and emails being used for sexual and homophobic harassment of members.
"Cyber-bullying and harassment, whether of pupils or staff, is unacceptable and should be met with zero tolerance. It can destroy health and careers.
"Too often when challenged about their children's inappropriate use of technology, parents regard it as harmless fun or claim that it is nothing to do with the school because home computers and emails were used.
"The provision in the Education and Inspection Bill on discipline, which provides schools with the power to discipline pupils for incidents off site, undoubtedly will help.
"However, schools need to ensure that such behaviour is mentioned explicitly in the discipline policy with a clear message to parents and pupils of zero tolerance.
"The government should take the opportunity when the guidance is issued to schools to advocate its application to staff."
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