Newspaper editors have been warned by David Cameron that they must act “urgently” to set up an independent press regulator.
The prime minister took part in a summit of senior industry figures at Number 10 to hear proposals for a new regime not backed by law.
Culture secretary Maria Miller has made clear that the option of legislation called for by the Leveson Report remains an option if progress cannot be made.
"I've just spoken to newspaper editors in No 10 — telling them they need to set up an independent regulator urgently," Mr Cameron wrote on Twitter.
Speaking after taking part in the high-level meeting, Mr Cameron said he had made clear that "the clock is ticking" for the industry to agree action.
"They have got to do it in a way that absolutely meets the requirement of Lord Justice Leveson's report," he said.
"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."
The prime minister has expressed "serious concerns and misgivings" about resorting to any form of statutory underpinning for press regulation.
But with Labour and the Liberal Democrats united in favour, his own backbenches split and phone-hacking victims leading a campaign for full implementation, he is under huge pressure.
An online petition launched by campaign group Hacked Off has so far attracted more than 135,000 signatures in favour of statutory underpinning.
Mrs Miller told MPs last night that change has to happen either "with the support of the press or — if we are given no option — without it".
Action "would include legislation" if industry proposals fall short of Leveson's principles, she said, warning against a "puppet show with the same people pulling the same strings".
Lord Hunt - who chairs the existing Press Complaints Commission – went into the talks claiming the support of 120 publishers, representing 2,000 editors, for a new independent regulator.
He believes legally-enforceable membership contracts could be used to give the new system force and avoid the need for statutory backing. Officials at Mrs Miller's Culture Department are drawing up a draft Bill to enact Leveson's recommendations in full.
But she has indicated that she expects it to provide confirmation of concerns about the complexity and potential negative impact on press freedom.
Labour is drawing up its own draft legislation to demonstrate that Leveson's recommendations could be implemented without the difficulties feared by ministers.
The Opposition's Bill is expected to be completed before Christmas, paving the way for it to force a Commons vote by the end of January if no agreement is reached in cross-party talks.
Daily Telegraph editor Tony Gallagher said the summit was attended by 19 editors and industry representatives, nine Whitehall officials and four ministers, including the prime minister and the culture secretary.
"It felt like the summoning of the Five Families in The Godfather," he joked on Twitter.
Labour leader Ed Miliband, who met Hacked Off representatives including phone-hacking victims in his office as the summit went on in Downing Street, said they wanted "more than good intentions" from the press.
"What I heard from the victims of sections of the press is that they are pleased there are good intentions from the editors but they want more than good intentions," he said.
"They want the force of law to make sure those good intentions are turned into reality."
Nick Clegg, who said he supported Leveson's recommendations, said he would enter cross-party talks in good faith.
Speaking on a visit to a school in south London, the Deputy Prime Minister said: "The key thing now is to get on with it. Of course we have our different views in response to the Leveson report and I made mine clear last week. The Prime Minister has his views," he said.
"We should not allow this to become a gridlock between politicians."
PA