Harriet Harman is urging ministers to work together with Labour to reform the regulation of the press.
The Labour deputy leader said Lord Justice Leveson's report on media standards and ethics - due out on Thursday - potentially offered the best chance to deal with an issue which politicians of all parties had struggled with for decades.
Addressing the Parliamentary Labour Party (PLP) at Westminster, she said it was important that no one sought to exploit the judge's report for political advantage.
Her comments came after foreign secretary William Hague became the latest senior Conservative to hint he would be reluctant to support statutory regulation of the press, saying they should "err on the side of freedom".
More than 40 Tory MPs are now preparing to publish a letter calling for a tougher system of self-regulation by the press rather than a statutory framework.
Labour, in contrast, is arguing for a system of regulation which is independent of both the press and the government but with "statutory underpinning".
Party sources said that in her comments to the PLP, Ms Harman echoed Labour leader Ed Miliband who called for Lord Justice Leveson's recommendations to be implemented provided they are reasonable and proportionate.
"What we want to see is proper redress of complaints," she was said to have told the meeting.
"As long as they are reasonable and proportionate they offer the best chance for all the parties to solve problems that have been with us for decades."
Downing Street has said Mr Cameron is keeping an open mind and would make no decisions before he has seen the report arising from the Leveson Inquiry which he set up in the wake of last year's phone-hacking scandal.