Campaigners such as the actor Hugh Grant have called for a state-appointed regulator to govern the press following the phone hacking scandal.
But the group of leading politicians say that such a system would endanger freedom of speech.
Lord Justice Leveson will today (November 28) submit his report to David Cameron, outlining the findings of his inquiry into the culture, practices and ethics of the press, along with his recommendations for a new regulatory system. The report will be published on Thursday.
However, the group of politicians - which includes eight former cabinet ministers, London Olympics chairman Lord Coe and Downton Abbey writer Lord Julian Fellowes - have written to The Guardian and The Daily Telegraph calling for a stronger system of self-regulation.
He was asked to produce a list of recommendations for a more effective regulation of the press, but in a way that would protect its independence and encourage high-quality journalism.
Currently, the press is self-regulated by the Press Complaints Commission (PCC), but that body has been criticised as being ineffective.
Leveson is widely expected to recommend some form of statutory regulation overseen by an independent body. But the group of MPs and peers believe that this could be detrimental to free speech.
In their letter, they say: "As parliamentarians, we believe in free speech and are opposed to the imposition of any form of statutory control even if it is dressed up as underpinning."
"No form of statutory regulation of the press would be possible without the imposition of state licensing - abolished in Britain in 1695," the group said.
"State licensing is inimical to any idea of press freedom and would radically alter the balance of our unwritten constitution.
"There are also serious concerns that statutory regulation of the print media may shift the balance to the digital platforms which, as recent events have shown through the fiasco of Newsnight-Twitter, would further undermine the position of properly moderated and edited print journalism."
The group instead back a proposal by former PCC chairmen Lord Hunt to create a "totally new" version of the regulator, which would have the power to investigate cases and levy fines of up to £1 million.
They also note: "[The] press abuse chronicled at Leveson was almost wholly about actions which were against the law. It demonstrated not a sole failure of regulation but rather of law enforcement."
The letter concludes: "Public debate will necessarily follow publication of the Leveson report and will be needed to provide confidence in a rigorous tough new system of self-regulation. Such a debate will lead to a speedy way of establishing a new self-regulatory regime that can restore confidence in the press."
However, some Liberal Democrat and Labour MPs have backed the call of campaigners for some sort of state regulation.
Actor Hugh Grant has consistently been the subject of negative press attention over the years, leading to him being a vocal campaigner in the Hacked Off group.
Grant, who will tonight be seen in Channel 4 documentary Hugh Grant: Taking on the Tabloids, has repeatedly said that the system of self-regulation through the PCC "has been seen again and again to fail".
He has backing from other celebrities and hacking victims such as Charlotte Church and Jude Law, but insists that he is campaigning on behalf of "ordinary people" who have fallen foul of the hackers, such as the Millie Dowler family,
The actor wants a state-appointed regulator to oversee the press, in the same way that Ofcom regulates TV, telecoms and some parts of the media.
> Leveson: State regulation 'slippery slope', warns senior Tory
Speaking to the BBC's Andrew Marr programme, he said: "Otherwise, the danger is that newspaper editors will just say, 'What is this new institution, this new body, this new regulator? We're not doing what you say. We're not paying your fines'."
TV presenter Anne Diamond, who has also been the victim of press intrusion, told BBC Breakfast that "self-regulation has been given its chance and it hasn't worked".
"The only way to have some real teeth behind some agreed code of conduct is to have some kind of statutory underpinning... You have to change the culture and the enforcement," she said.
Downing Street has said that prime minister David Cameron is keeping an 'open mind' until he sees the Leveson report, although it has been claimed that he has already ruled out state regulation of the press.