Liberal Democrat leader Nick Clegg said a press regulation plan devised with Labour leader Ed Miliband would "deliver what Leveson wanted", as he invited Tory MPs to back it.
"I hope the approach we are publishing today plots a middle course between the dangers of doing nothing and the fears some people have of a full-scale legislative approach," he said.
"This is a system that both myself and Ed Miliband back, and that I believe Conservative MPs can also support."
Clegg called the Charter a "strengthened version" of David Cameron's plan for press regulation, which the Prime Minister championed yesterday after halting cross-party talks on the issue.
MPs will choose between the two approaches in a series of votes on Monday.
Newspapers will invite members of the public to review the way papers are written in the wake of the Leveson Report, it has been announced.
The Editors' Code of Practice Committee said it plans to review the journalists' code in a series of new initatives following Lord Justice Leveson's recommendations for the reform of press regulation.
Five lay individuals will be appointed to the committee of 13 editors, along with a chairman and a director of the new press regulator.
The actor High Grant has urged the Government to establish an independent media regulator on the back of Lord Leveson's inquiry into press ethics.
"Self-regulation of the press is a system that has been proven to fail for 50 years," the actor told the BBC's Andrew Marr Show.
"What could come out of Leveson is an independent regulator. I do not see the slightest danger to freedom of speech from it."
Grant said he fears David Cameron's government could ignore the findings of the inquiry.
"Suddenly, sinisterly, a few weeks ago we start to get weird rumblings from (the Government) that Leveson is a waste of time," he said.
The Cabinet Office said it has no record of a disputed telephone call in which Rupert Murdoch claims Gordon Brown said he was declaring war on the media mogul.
Mr Murdoch told the Leveson Inquiry in April that Mr Brown accused the Murdoch empire of declaring war on the government, which he had no choice but to "make war" in turn. Mr Brown responded this week at the Inquiry saying that the September call never took place. A Cabinet Office spokesman said:
" We can confirm that there is a record of only one call between Mr Brown and Rupert Murdoch in the year to March 2010. That call took place on the 10th of November 2009."
Speaking at the Leveson Inquiry today, Lord Mandelson described Rebekah Brooks as known for her "persistence, charm and manipulative skills" - adding: "Although some people might say that's rich coming from me."
"She's very good at keeping in touch. I mean, obviously famously by text but in other ways. She doesn't hold back."
Brooks had "ease of access" to then prime minister Tony Blair, he said.
He also acknowledged that both Mr Blair and his successor Gordon Brown "arguably" became "closer than was wise" to Mr Murdoch.
Alastair Campbell has revealed why the Labour party decided to court The Sun rather than other newspapers, when he was appointed as Tony Blair's director of communications.
Well it probably fell into the category of the only one that might... shift position.
I couldn't have ever imagined the Daily Mail. So our approach... was just to kind of stop them being quite so vile.
Our approach with papers like the Express would have been to engage with them, but I would never have expected the Express to come out for the Labour party.
And the broadsheets were in a slightly different space...So the Sun, in a sense, was the only one that was in this really odd space.
Although we set ourselves that objective, I think if you had asked me in 1994 did I think the Sun would back us in 1997, I would probably have said no.
Tony Blair's former press advisor Alastair Campbell has been appearing for a second time before the Leveson Inquiry.
Robert Jay QC made the ex spin doctor blush by reading extracts from Mr Blair's autobiography, where he described the difference in style between Mr Campbell and Peter Mandelson.
Former cabinet secretary Lord O'Donnell has urged the Leveson Inquiry to issue guidelines to help opposition parties deal with the press.
He said: "I think you would want to put it to the leaders of all the parties, 'Here is a set of rules that we think opposition parties should abide by'".
News International's barrister Rhodri Davies accuses Robert Jay, counsel for the Leveson Inquiry, of trying to make out that The Sun has "sinister" motives for its decisions to back certain politicians.