Culture Secretary Maria Miller has warned internet trolls to expect arrest if they threaten or insult people online.
In a speech to the Oxford Media Convention, the Cabinet minister said there was a "straightforward principle" that "the rules that apply offline are the same rules that apply online".
She said: "The internet isn't a 'Second Life', it isn't something where different rules apply, where different behaviour is acceptable - it isn't the wild west."
In her speech, about the "rights and responsibilities of the internet age", she said: "Whether it is images of child abuse or terrorist material we will use the full force of the law, national and international, to take down that content and pursue the perpetrators.
"If you vilely insulted, or threatened to attack someone in person on the street, you do so expecting to be arrested and charged. The same already applies on social media."
Referring to the recent jailing of a man and a woman who subjected feminist campaigner Caroline Criado-Perez to online abuse, Ms Miller said that "being online does not mean the law doesn't apply to you. And the law is being used. Last year 2000 people were prosecuted for sending electronic communications that were grossly offensive or menacing."
She said: "If you wanted to see a film or listen to a CD, you wouldn't sneak into a shop and steal it off the shelf, so why do the online equivalent and download it illegally?
"It's about good citizenship... as well as what's legal and what's not."