David Cameron has warned newspaper editors that they must act "urgently" to set up an independent press regulator.
The Prime Minister met with newspaper editors in Downing Street in the wake of the Leveson Report on press standards and ethics.
Senior industry figures at the summit, which was also attended by Culture Secretary Maria Miller, argued against having a system underpinned by law.
And they set out their progress towards the creation of a new independent watchdog in the hope this will go far enough to avoid legislation.
Mrs Miller has warned that any failure to unite behind a sufficiently tough and independent self-regulatory body could leave the Government no choice but to legislate.
The Prime Minister adopted a harsh line with the group, making clear that they only have a few months to get their house in order.
Speaking afterwards, he said: "They have got to do it in a way that absolutely meets the requirement of Lord Justice Leveson's report.
"That means million-pound fines, proper investigation of complaints, prominent apologies, a tough independent regulatory system.
"And they know, because I told them, the clock is ticking for this to be sorted out."
Mrs Miller added: "There was unanimous agreement that what we need now is for the press to go forward with developing a tough independent self-regulatory body.
"The challenge has been thrown down to them. They have responded positively. It is now for them to go away and to develop those plans.
"The industry will be setting that out in the next two days."
The Sun's editor Dominic Mohan, The Times' editor James Harding and Daily Telegraph editor Tony Gallagher were among the figures at the talks.
Mr Gallagher said on Twitter: "19 editors & industry reps, 9 mandarins, 3 ministers and 1 PM. We got coffee and still tap water. No beer & sandwiches."
He later added that it had "felt like the summoning of the Five Families in The Godfather".
Chris Blackhurst, the editor of The Independent, told Sky News that newspapers were very united and had recognised this was their final chance.
"We can't go through this again. This has to be the end... and something good is going to come out of this," he said.
The editor admitted that Mr Cameron had effectively done the industry "a favour" by not imposing statute and that it was not time for them to "give something back".
"We have got to come up with a strong system of independent self-regulation. We haven't got much time," he said.
The Prime Minister last week declared his "serious concerns and misgivings" about Lord Justice Leveson's recommendation of a new system supported by law.
But he is under huge pressure from campaigners who are furious that he has rejected the central proposal of the report and are insisting on full implementation.
His own backbenchers are also split and the Liberal Democrats and Labour are currently mostly united in favour, raising the prospect of a damaging Commons vote.
An online petition launched by campaign Hacked Off has so far attracted more than 135,000 signatures in favour of statutory underpinning.
Press Complaints Commission chairman Lord Hunt says he already has the support of 120 publishers, representing 2,000 editors, for a new independent regulator.
He insists it is not necessary to back that up with legislation because newspapers could instead sign legally-enforceable membership contracts.
Officials at the Culture Department are drawing up a draft Bill to enact Lord Justice Leveson's recommendations in full.
But Mrs Miller has indicated that she expects it to confirm concerns about the complexity and potential negative consequences of statutory control.
Any legislation could be amended by future administrations to muzzle the press and would harm the UK's reputation abroad as an advocate of free speech, she told MPs on Monday.
However, Labour leader Ed Miliband is not backing down. He insisted on Tuesday that enacting Lord Leveson's proposals was "the right thing" because the new system had to be robust.
"We need the promises that have been made to be put into legislation so that what we actually have is independent self-regulation but we have the guarantee of law," he said.
"I do not believe and I wouldn't be supporting it if it was about restricting freedom of the press. This is actually about protecting the freedoms of ordinary people to go about their business and not face intrusion and harassment."