Culture Secretary Karen Bradley has said she wants a press regulator that maintains a free press while protecting victims of abuse, as it emerged that campaigners are legally challenging a Government consultation on the issue.
Two victims of press intrusion have joined investigative news website Byline Media in filing a claim for a judicial review, over the consultation on whether to proceed with part two of the Leveson Inquiry.
This is due to investigate News International and corrupt dealings between police and the press, as well as plans to force newspapers to pay opponents' legal costs in things like libel and privacy cases.
Speaking on the BBC Radio 4 Today programme, Ms Bradley said: "There are different views on what's the right thing to do now, to make sure we have the right press regulation.
"What I'm keen to make sure is we have press regulation that works, to make sure victims of press intrusion can have access to justice, cheap justice, to make sure they can see justice being done.
"But also that we have a free press, that enables the press to do the job that they have done so fantastically over so many, many centuries to keep the government to account and make sure that we have the thriving democracy that we do have."
Ms Bradley added that she would make a decision after analysing the responses to the Government's consultation, which closes in January.
Former Crimewatch presenter Jacqui Hames is one of the victims calling for a judicial review of the Government's consultation.
The other claimant is an anonymous phone-hacking victim.
Campaigners say the measures being consulted on have already been promised, while the consultation itself is biased.
Part two of Leveson Inquiry was to focus on corporate governance failures and unlawful conduct at News International, as well as the company's relationship with the Metropolitan Police.
Launching the consultation, the Government said it needed to judge whether continuing with part two of the inquiry "is still appropriate, proportionate and in the public interest".
The consultation is also looking at Section 40 of the Crime and Courts Act 2013.
This controversial measure would see newspapers which are not signed up to a recognised regulator pay their own and their opponents' legal costs, even if they won the court case.
The costs provision has been enacted by Parliament, but has not yet been commenced by the Culture Secretary.
This was a recommendation from part one of the Leveson Inquiry, which was published four years ago.
A Department for Culture, Media and Sport spokeswoman said: "We can confirm that an application has been made to judicially review the consultation.
"The Government is considering its response."
Regulator Impress has received formal approval from the Press Recognition Panel, which was set up in the wake of the Leveson Inquiry.
It is funded partly by Max Mosley, the former motor racing boss, who was a victim of a newspaper sting.
But most newspapers have signed up to rival regulator the Independent Press Standards Organisation, the press-funded body which did not seek official recognition.
Ms Hames joined Crimewatch after 30 years with the Metropolitan Police, where her ex-husband, David Cook, was also a detective.
Mr Cook was involved in probing the murder of private investigator Daniel Morgan, whose business partner at the time, Jonathan Rees, had links to News of the World.
Ms Hames has alleged that her confidential police personnel file was sold to private investigator Glenn Mulcaire, who worked for the News of the World, and that the newspaper put her and Mr Cook under surveillance because of their role in investigating Mr Morgan's murder.