Lord Just Leveson launches the inquiry in London Press Association

Lord Justice Leveson, appointed by David Cameron to look into the fallout from the phone-hacking scandal, warned yesterday that he may not be able to complete the first part of the inquiry within the planned timescale of a year because its goals had been widened "quite substantially".

Senior parliamentarians said it was possible the full inquiry, including an investigation into any criminal wrongdoing, may take until close to the 2015 general election.

Leveson said he would strive to meet the deadline, but it could require great discipline by his fellow inquiry members since the widening of the terms of reference.

His remarks reveal alarm inside the inquiry at the scale of their task and the requirement to produce some policy conclusions before inquiring in detail at the scale and causes of the malpractice.

Keith Vaz, the chair of the home affairs select committee, said he expected the inquiry may not be completed until just before the next election, partly because the second part of the inquiry – into specific wrongdoing by individuals – would have to wait for the outcome of a criminal inquiry.

Vaz said: "What Lord Justice Leveson will want to do is write the script for press regulation, relationships between politicians and the press and all those other issues for some time to come."

Leveson was speaking as his inquiry team met for the first time in London. He said: "In the first instance the inquiry will focus primarily on the relationship between the press and the public and the related issue of press regulation."

He said he would have powers to compel named witnesses to attend and would be discussing the extent to which he could investigate media wrongdoing before criminal inquiries were completed with the director of public prosecutions.

His remarks suggest figures such as Cameron and Rupert Murdoch or his son James will be compelled to give evidence under oath.

In a statement, Leveson stressed he would not be confining his inquiry to the News of the World. "It may be tempting for a number of people to close ranks and suggest that the problem is or was local to a group of journalists then operating at the News of the World but I would encourage all to take a wider picture of the public good and help grapple with the width and depth of the problem.

"The focus of the inquiry is the culture, practices and ethics of the press in the context of the latter's relationship with the public, the police and politicians."

"At some stage there needs to be a discussion of what amounts to the public good, to what extent the public interest should be taken into account and by whom."

He explained the inquiry would be holding seminars on press relationships with the police, politicians and the political process in the autumn.

In one of his few specific commitments, he said one aspect of the inquiry may be why "no action was taken in 2006 following a report by the information commissioner" into the use of private detectives and eavesdropping.

He stressed the 2005 Inquiries Act gave him powers to require witnesses to attend and provide documentation. That would give him the means to order UK witnesses to attend, but he said no witness should see such an order as a reflection on their willingness to co-operate.

He said he would not, at this stage, be compelling editors or proprietors to provide files on which they had based stories into "the utterly inappropriate behaviour of small sections of the press" but "I would rather invite editors, proprietors of magazines and journalists to assist me by providing a wide range of examples of what is contended to be inappropriate for one reason or another across the fullest range of titles." [see footnote]

Leveson addressed concerns that he may be seen as excessively close to News International because he has attended two parties at the home of Matthew Freud – the publicist who is married to Elisabeth Murdoch, the daughter of Rupert Murdoch.

He said he had met Freud by chance at a dinner in February 2010 when Freud had offered to do some work free of charge on the issue of public confidence in sentencing. Leveson is chair of the Sentencing Council. He said he had not spoken with anyone from Freud Communications since January 2011.

Another inquiry member, Lord Currie, said although he was a past chairman of Ofcom, the broadcasting regulator, that did not mean he favoured statutory regulation. In a statement he said: "I believe self-regulation with good governance in place can be superior. Each case needs to be judged on it merits."

• This article was amended on 1 August 2011. A sentence wrongly gave the impression that Lord Justice Leveson would not be asking editors and proprietors to submit examples of "the utterly inappropriate behaviour of small sections of the press". This has been corrected.