Two newspapers published articles about the arrest of a man over the killing of Jo Yeates which were in contempt of court, the High Court has been told.
Attorney General Dominic Grieve said he wanted a prison sentence awarded or another "appropriate penalty".
The Sun and Daily Mirror dispute Mr Grieve's claims, and deny contempt.
He said the articles meant that had Christopher Jefferies, who was arrested and then released, been charged, he would not have had a fair trial.
Mr Jefferies, who was Miss Yeates' Bristol landlord, was arrested in December 2010 but was later released without charge.
Mr Grieve, the government's chief legal adviser, said the stories overstepped the mark and if Mr Jefferies had gone on to be charged, they would have posed a "substantial risk of serious prejudice" to any trial he might have faced.
He added that the articles contained material which would not have been placed before a jury as "admissible evidence".
In written documents before the court, Mr Grieve said his concerns related to articles in the Mirror on December 31 and January 1 and an article in the Sun on January 1.
He said the articles contained material which was "exceptionally adverse and hostile" to Mr Jefferies and that Mr Jefferies challenged material contained in the articles and had made a separate libel complaint.
Mr Grieve said he had warned the media about coverage "in the context of [Mr Jefferies'] arrest" during a BBC radio interview on December 31.
The retired teacher was "entirely innocent", Mr Grieve added.
Lawyers representing Mirror Group Newspapers (MGN) - publishers of the Mirror - and News Group Newspapers (NGN) - publishers of The Sun - have outlined their defence in written submissions given to judges.
BBC home affairs correspondent Matt Prodger said the case has far-reaching implications for the future of the Contempt of Court Act, which restricts the publication of material that could seriously prejudice a trial.
Miss Yeates vanished after returning to her basement flat in Bristol's Clifton area on 17 December.
Her body was found on a grass verge about three miles away on Longwood Lane in Failand on Christmas Day.
Miss Yeates' neighbour, Vincent Tabak, 33, from the Netherlands, has admitted manslaughter and is awaiting trial accused of murder.
Miss Yeates' landlord, Mr Jefferies, who was the subject of media scrutiny after he was arrested, is also suing six national newspapers in the civil courts.
Our correspondent said the law of contempt has become the subject of much debate in recent months.
He said both the competition of 24-hour news and a relatively unregulated internet pose a significant challenge to the system of fair trials, which relies on juries reaching a verdict based only on the evidence they hear in court.
Our correspondent said the hearing had now concluded.
The three judges, including Lord Chief Justice Lord Judge, have reserved judgement until a later date.