Controversial plans which could see newspapers landed with opponents' legal costs even if they win in court are an attempt to "blackmail" the press into signing up to a "state-sponsored" regulator, Sun editor-in-chief Tony Gallagher said.
Ministers are consulting on whether to implement the measure, which Mr Gallagher said was "insane" and went against the principles of natural justice.
But phone hacking victim and former Crimewatch presenter Jacqui Hames said the public wanted the press to be independently regulated and it would be a betrayal if the full package of reforms introduced after the Leveson Inquiry was not brought into effect.
Ms Hames has launched a legal challenge to the Government's consultation, which will look at whether to press ahead with implementing Section 40 of the Crime and Courts Act 2013.
This measure would see newspapers which are not signed up to an officially-recognised regulator pay their own and the plaintiff's legal costs, even if they were successful in court.
The consultation, which ends on January 10, is also examining whether to go ahead with the second part of the Leveson Inquiry, which would look at wrongdoing in the police and press.
Mr Gallagher said part two of Leveson would be "essentially a sideshow" because the media landscape had changed so much since the original inquiry.
He said: "The Government is perfectly at liberty to decide to have it, but I think it would be a waste of time and money and effort."
On Section 40, Mr Gallagher said: "Essentially it is an attempt to blackmail newspapers into joining the government's regulator, a state-sponsored regulator, and no self-respecting newspaper worth its salt wants to be part of a state-sponsored regulator because you are then on the road to giving MPs power and the whip hand over the press."
Warning of the impact if the costs provision was implemented, he said: "A newspaper could report the conduct of a terrible MP, that MP could then bring a case for libel against a newspaper. He or she could lose that libel case and yet, because we are not members of the state-sponsored regulator, we would then be liable for the MP's costs.
"That offends all principles of natural justice. It's insane."
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 (Ipso), the press-funded body which did not seek official recognition - and would therefore be faced with paying plaintiffs' costs under the Section 40 provisions.
Ms Hames told Today that the second part of the Leveson Inquiry was necessary because the original probe could not examine criminal cases which were yet to come before the courts.
"There were any number of questions which are still waiting to be asked," the Hacked Off campaigner said.
She insisted that the Section 40 measures were one part of an overall package of reforms which came out of the Leveson Inquiry and insisted that any officially-recognised regulator would remain independent of government.
Dismissing the concerns of the press, she said: "They do not want to be independently regulated - and independently is the key word."
Independent regulation was what the public and victims of press abuse wanted to see, she added.
If Section 40 was not implemented she said she would be "absolutely appalled" and she would feel "betrayed" if it did not go ahead.