Nick Clegg will make a separate statement to the House of Commons after the Leveson report is released, parliamentary authorities say, apparently confirming that the coalition has failed to reach agreement on its response.

Sources stressed that the deputy prime minister and David Cameron had reached an agreement on some aspects of the government's response, which will focus on how to reform press regulation, but it nevertheless indicates a significant split in the coalition. It is unprecedented for the pair to make rival statements in the Commons on the same subject.

Leveson's 16-month inquiry into "the culture, practices and ethics of the press" will make recommendations on how regulation should be reformed and include criticisms of the police, press and politicians over the phone-hacking scandal and its aftermath, amid a fierce debate within Westminster and the media as to what the most appropriate model of reform should look like – whether a form of statutory regulation or a more robust model of self-regulation.

Clegg met Cameron on Wednesday to discuss their approach to the report. Cameron is expected to call for a tough new independent press complaints body capable of imposing fines, while keeping the option of statutory regulation on the table for a later date if the new regulatory body is not working.

Clegg held phone calls on Wednesday night with Lib Dem cabinet colleagues before a rare meeting of the coalition committee on Thursday morning to be attended by the most senior members of the cabinet, including the business secretary, Vince Cable, and the education secretary, Michael Gove.

After Clegg's decision to issue a separate statement was announced, a Lib Dem source insisted: "Do not look at this as some massive split on the issue, or the coalition at loggerheads. That's not where we are. Nick slept on this overnight and took the final decision this morning. He [took the decision to make a separate statement in the Commons] because, regardless of how the coalition committee goes, people are going to be looking ahead to cross-party talks and they are going to be talking about where the different parties and the different party leaders stand, and Nick thought it was right to seek an opportunity to set out his stall as one of the three main party leaders."

Cameron is minded to demand a toughened up form of independent regulation, but to give the newspaper industry six months to put its house in order or face statutory controls. There are key figures in No 10 advising him that he cannot be seen to be soft on Tory-inclined newspapers, even if it sours relations between him and their proprietors.

Conservative cabinet sources on Wednesday night accused the Liberal Democrats of playing a dangerous game by appearing to back state regulation before the publication of the 2,000-page verdict on media ethics.

In a sign of the tensions before what will be a landmark day for politicians, the media and the police, Lib Dem sources said: "This is not a problem for us – the person who has got a difficulty is David Cameron." A senior Tory source said: "Labour and the Liberal Democrats are backing statutory regulation, even before they have seen the report. The Liberal Democrats are playing a dangerous game."

Leveson has to come up with a system that will cover the whole of the press, whether voluntary or mandatory. Newspaper owners and editors unanimously argue that anything akin to statutory regulation could amount to the censorship of free speech.

But the culture and media secretary, Maria Miller, has told leading newspaper figures, such as Lord Hunt, the chairman of the Press Complaints Commission (PCC), that their proposals for independent regulation are inadequate, too close to the industry, and will need to be strengthened.

Leveson's report is expected to contain major criticisms not just of the press but also of the Metropolitan police over their handling of the phone-hacking scandal and relations with the media.

A warning letter to the Met says the force's own actions allowed a perception to emerge that certain media organisations were favoured.

Set up by Cameron and Clegg in the wake of the revelation that the mobile phone belonging to the missing schoolgirl Milly Dowler had been hacked by the News of the World, the inquiry will examine relations of power between the press and the public, politicians and police.

The inquiry heard from 184 witnesses and accepted hundreds of written submissions in nine months of hearings. It exposed the excesses of the press in pursuit of stories about celebrities, crime victims and ordinary members of the public caught in the tabloid net along with a cosy relationship between a succession of prime ministers and News International.

It also raised the question of why politicians, police and the PCC had failed to investigate the practice more thoroughly when the first allegations of News of the World hacking were raised by the Guardian in July 2009.

Critics of Rupert Murdoch's News Corporation, the owner of the tabloid that was closed amid public outcry over the Milly Dowler revelations, argued that his company was so powerful that ministers, chief constables and regulators could not reign him in.

The PCC remains in place but its authority as a regulator has been severely undermined by the hacking scandal.

Two polls by ComRes, one for ITV and another for BBC Radio 5 Live, showed firm support for independent regulation backed by law. The ITV poll showed 51% of the public think the government should introduce statutory regulation of the media. Just 20% disagree and 30% said they didn't know. The BBC poll showed 66% of respondents had not very much trust, or no trust, in British newspapers telling the truth. Almost half (47%) of those questioned said they most wanted a regulatory body for newspapers where the rules were agreed and enforced by the courts.