More than 80 MPs and peers have urged the man carrying out an inquiry into UK media standards not to recommend a press regulation law.
The cross-party group, including eight former cabinet ministers and London Olympics chairman Lord Coe, says any such move would damage press freedom.
Lord Justice Leveson is due to publish his report on Thursday.
The Leveson Inquiry was established by the prime minister in July last year and looked into the culture, practices and ethics of the press.
It was commissioned following allegations of illegal phone-hacking at the News of the World.
Prime Minister David Cameron, who has already warned politicians not to pre-empt its findings, will receive his copy of the report at lunchtime on Wednesday - 24 hours before its details are made public.
Lord Justice Leveson was asked to produce a list of recommendations for a more effective policy and regulatory regime for the press, which would preserve its independence while encouraging higher ethical and professional standards.
At the moment the press is self-regulated through the Press Complaints Commission (PCC).
Lord Justice Leveson is widely expected to recommend some form of statutory regulation overseen by an independent body.
But the politicians, led by former Labour home secretary David Blunkett and Conservative MP Conor Burns, argue in their letter this could be detrimental to free speech, saying: "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."
They add: "No form of statutory regulation of the press would be possible without the imposition of state licensing - abolished in Britain in 1695. 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 - which includes Commons culture media and sport committee chairman John Whittingdale, Downton Abbey writer Lord Fellowes, former Commons Speaker Baroness Boothroyd and ex-cabinet ministers Lord Tebbit, Liam Fox, John Redwood and Peter Lilley - has written to the Guardian and the Daily Telegraph,
It backs a proposal from former PCC chairman Lord Hunt and Lord Black, one-time chairman of the body that finances the commission, for a "totally new" version of the regulator.
They propose an independent body with increased powers to investigate complaints and illegal behaviour, levy fines of up to £1m and award compensation, and enforce membership by newspapers for the first time.
Some campaigners say the current system of self-regulation, overseen by the Press Complaints Commission, is inadequate and that tougher rules are needed to curb newspapers' excesses.
Earlier this month, 42 Conservative MPs and peers wrote to the Guardian arguing in favour of some form of statutory underpinning for press regulation.
Broadcaster Anne Diamond, who gave evidence to the Leveson Inquiry about her experience with the press, 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."
The actor Hugh Grant, who has been campaigning for stricter press regulation, told Breakfast: "What people are campaigning for is an end to newspapers being able to regulate themselves... because that is what has resulted in the kind of abuses of people like the Dowlers, the McCanns, Christopher Jefferies."
He added: "The only industry in this country which is allowed to regulate itself is the newspaper industry... We need a proper regulator, an independent regulator, meaningful, that will need some statute to oblige newspapers to sign up to it."
Martin Moore, director of the Media Standards Trust charity, said the challenge for Lord Justice Leveson was to balance the need for some sort of redress for "ordinary people" with freedom of the press.
It is up to David Cameron to decide whether to implement Lord Justice Leveson's recommendations.
Downing Street has said the prime minister was "open-minded" about the future regulation. Previously he said he intended to implement the findings of the Leveson inquiry, provided they were not "bonkers".
But the BBC's political editor Nick Robinson says the coalition is preparing for the possibility that it may be divided by the report's recommendations, with Deputy Prime Minister Nick Clegg less likely to be hostile to Lord Justice Leveson's proposals.