The pictures, which can be impossible to remove because they are quickly reproduced on other sites, can destroy careers and relationships, experts said.
A number of states in America have already introduced laws, with a number of arrests being made. However, there is no specific law in the UK, only laws preventing "malicious communications", which usually involve written abuse not pictures, and harassment, but these usually require a number of offences.
The Ministry of Justice is expected to look at how existing laws could be amended to outlaw the distribution of sexual images without consent.
It emerged last week that complaints about abuse and anti-social behaviour arising from Facebook, Twitter or other forms of social media make up "at least half" of calls passed to police. Chief Constable Alex Marshall, the head of the College of Policing, claims that it represents "a real problem for people working on the front line of policing".
'It's clearly becoming a bigger problem in our society'
Speaking in Parliament yesterday, Mr Grayling said: "It's clearly becoming a bigger problem in our society. What I'd say to you today is the Government is very open to having a serious discussion about this with a view to taking appropriate action in the autumn if we can identify the best way of doing so."
Mr Grayling's comments came in response to a question from Maria Miller, the former culture secretary who has been campaigning for a change in the law. Mrs Miller, who resigned following an investigation into her expenses claims, said: "Posting revenge pornography on the internet is an appalling crime. Do you agree with me that the law needs to change to ensure that perpetrators are properly punished and that perhaps the Criminal Justice and Courts Bill, currently in the Lords, could provide the Government an opportunity to do just that?"
It is understood that ministers are considering whether an amendment to the Bill could be used. Lord Faulks, a justice minister, this week told the House of Lords that he was "anxious to accommodate some of the concerns" over revenge pornography.
A number of tragic incidents
There have been a number of tragic incidents. In 2009, Emma Jones, 24, a teacher from Caerphilly, Wales, killed herself because she believed her former boyfriend had posted pictures of her on Facebook. She was working in Abu Dhabi and feared she would be jailed in the Muslim country. At an inquest, her former partner denied the claim and the coroner said he could not be blamed for her death.
Martin Horwood, the Liberal Democrat MP for Cheltenham, said: "We do need a change in the law because the current laws cover extreme obscenity and pictures taken without consent - neither of which necessarily apply to revenge porn - but don't provide a legal basis for search engines to remove these sites from results. And it's those search engine results that are the real killer for innocent women trying to apply for jobs or just live their lives in the internet age."
'Just another form of coercive control'
Polly Neate, the chief executive of Women's Aid, said: "Any attempt to tackle revenge porn must also take account of all other kinds of psychological abuse and controlling behaviour, and revenge porn is just another form of coercive control."
Holly Dustin, from the End Violence Against Women Coalition, said: "We warmly welcome the Government looking at revenge porn which is enabled by technology, as with other forms of abuse of women and girls online."
But Emma Carr, of Big Brother Watch, said: "The Government must ensure that any new laws created to police what is posted on the internet is done so with a clear head and not in the heat of the moment. Judging what is and isn't acceptable ... is a very difficult decision to make and is often a matter of individual opinion. Asking the police to make that judgment call could be a recipe for disaster.
Next trending article: Sex case diplomat 'hasn't got away with it'
