Possessing and accessing extreme internet pornography could become illegal under government proposals.
Murder victim Jane Longhurst's family has campaigned for new laws
Distribution of extreme pornography is illegal in the UK but this does not affect foreign websites, so new laws could ban possession of it in Britain.
The Home Office and Scottish Executive are consulting on whether new laws are needed and what should be covered.
The idea was welcomed by the family of Jane Longhurst, of Hove, murdered by a man addicted to violent net porn.
The aim is for a new offence of possessing violent and abusive pornography, which could be punishable by up to three years in prison, Home Officer Minister Paul Goggins told BBC Radio 4's Today programme.
Mr Goggins said such images were "extremely offensive to the vast majority" and had no place in society.
If it is found that the law can be strengthened to cut violent pornography from our society, then we will take action
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A Home Office spokeswoman added the proposed law included deliberately viewing such images which meant "effectively downloading" the information on to the computer.
The new laws would not affect people who came into contact with pornographic material by accident.
"These forms of violent and abusive pornography go far beyond what we allow to be shown in films or even sold in licensed sex shops in the UK, so they should not be available online either."
UK-based websites and other distributors face prosecution under the Obscene Publications Act 1959.
Mr Goggins told BBC Radio 4's Today programme: "We do feel it necessary to provide some form of protection for the public, particularly for young children increasingly accessing the internet.
"It is very important that we protect them from accessing these kinds of extreme pornographic images.
He said there was also a responsibility to "reduce demand" for this kind of material, both to protect those who were abused in its making and the public.
He added that accidentally accessing such material would be a defence.
Cathy Jamieson, Scottish Executive Justice Minister, said: "Violent pornography is abhorrent.
"If it is found that the law can be strengthened to cut violent pornography from our society, then we will take action."
The proposals were welcomed by Metropolitan Police Commander Dave Johnston.
Mr Johnston, a representative of the Association of Chief Police Officers, said: "The internet is being targeted more and more by those who create sites that specialise in sexual violence and other types of extreme perversion."
The fact many sites were outside the UK made investigations very difficult and the creation of new offences would "assist greatly", he said.
"The fact that it is available over the internet should in no way legitimise it," he said.
However, Dr Chris Evans, founder of a group called Internet Freedom, told the Today programme that no material should be banned and people should be able to make up their own minds.
"There is a recognition, even in the proposals, that 60 years of research into media effects shows no conclusive evidence that violent images cause violent acts, so I think that the very idea that we need to ban it doesn't hold water," he said.
"But I think the serious problem with it is the assumption that ordinary people cannot be trusted to make up their own minds about what they read, watch or see."
But Mr Goggins argued that they could "certainly point to cases" where viewing such images had an effect - such as in the brutal murder of Jane Longhurst.
Miss Longhurst was murdered in Hove, Sussex, two years ago by a friend's boyfriend, Graham Coutts, who had spent hours viewing images of women being strangled and raped.
Ms Longhurst's mother Liz, of Reading, Berkshire, was shocked that such images were freely available over the internet and has campaigned for new laws.
Martin Salter, Labour MP for Reading West, praised Mrs Longhurst's "courage and motivation" and said he was pleased the legal "loophole" of the internet could be closed.
He said Mrs Longhurst had sought to ensure others "did not experience her dreadful loss when her lovely daughter Jane was murdered by a sick, self-confessed addict of extreme internet porn".
The Liberal Democrats home affairs spokesman Mark Oaten urged the government to provide a "very clear and succinct definition" of what constitutes violent and abusive pornography.
"Sensible measures which protect children from extreme sites should be warmly welcomed. However, the government must avoid creating a nanny state or introducing laws that can't be enforced," he said.
Consultation on the proposals is open to everybody, including interested parties and the public, and people can give their views until 2 December.