Lord Justice Leveson is examining the culture and practices of the press following the hacking scandal.

Despite the warning, he said he had "absolutely no wish to stifle freedom of speech and expression".

Meanwhile, a private detective's notebooks suggest he hacked phones for the Sun and the Daily Mirror.

The hearing heard Glenn Mulcaire wrote names in his notes which recorded the voicemails he illegally intercepted, which suggested he worked for those newspapers as well as for a series of News of the World journalists.

Hearings will later examine the extent of unlawful conduct by the press, and the police's initial hacking investigation.

This second phase will wait until after the current police investigation into News of the World phone hacking, and any resultant prosecutions.

Lord Justice Leveson said concerns had been raised that the press might target those who spoke out against it during the inquiry.

"I have absolutely no wish to stifle freedom of speech and expression, but I anticipate that monitoring will take place of press coverage over the months to come.

"And if it appears that those concerns are made out, without objective justification, it might be appropriate to draw the conclusion that these vital rights are being abused, which itself would provide evidence of culture, practice and ethics which could be relevant to my ultimate recommendations."

In opening remarks, he reiterated: "I fully consider freedom of expression and freedom of the press to be fundamental to our democracy. But that freedom must be exercised with the rights of others in mind."

He said the press provided "an essential check on all aspects of public life".

"That is why any failure within the media affects all of us. At the heart of this inquiry therefore may be one simple question - who guards the guardians?"

Counsel to the inquiry, Robert Jay QC, has been outlining the inquiry's terms of reference and the reasons for its establishment.

He said what could be justified as being in the public interest and how, lay at the heart of the hearings.

The inquiry had not yet seen any examples of phone hacking by media that could "even start to be justified on public interest grounds", Mr Jay said.

"A constant theme will be the alleged subterranean influences operated by the press on the democratic process."

'Body of evidence'

BBC political correspondent Ross Hawkins, who is reporting on the inquiry via twitter, says that Mr Jay has stated that "questions must be asked as to how high up in News International the metaphorical buck stops".

Mr Jay went on to say evidence is beginning to emerge that phone hacking was not limited to News International, our correspondent added.

The lawyer gave the hearing details of the notebooks belonging to Glenn Mulcaire, who was jailed with the News of the World's former royal editor Clive Goodman after they admitted intercepting voicemail messages on royal phones.

Some of his notes corresponded to News of the World employees, one of whom - referred to only as "A" - apparently made 1,453 separate requests for information from Mulcaire.

But he also wrote "The Sun" and a name relating to the Daily Mirror in his notebooks, the inquiry was told.

In total, about 28 legible corner names are legible in the 11,000 pages of notes which police seized from Mulcaire, which relate to a total of 2,266 taskings and the names of 5,795 potential victims, the inquiry heard.

The first witnesses are not expected to be called until next week.

The revelation earlier this year that Milly Dowler's phone had been hacked by the News of the World prompted Prime Minister David Cameron to establish the inquiry, and led to the closure of the tabloid.

Those giving evidence will include the parents of the murdered teenager and the parents of missing girl Madeleine McCann.

Fifty-three alleged victims have now granted core participant status, meaning they can be represented by a barrister, seek to cross-examine witnesses and make opening and closing statements during the inquiry.

BBC correspondent Peter Hunt says Milly's father, and MPs Denis MacShane and Chris Bryant are attending day one of the hearings.

Lord Justice Leveson is being advised by a six-member panel consisting of Liberty director Shami Chakrabarti, former Ofcom chairman Lord (David) Currie, former Channel 4 News political editor Elinor Goodman, ex-Daily Telegraph political editor George Jones, former Financial Times chairman Sir David Bell and ex-West Midlands police chief constable Sir Paul Scott-Lee.

Sun associate editor Trevor Kavanagh told Today he thought there was insufficient representation of the tabloid press on the inquiry panel.

"With such a very large part of the newspaper industry unrepresented, I think there is a risk that it will not look at the whole picture."

Lord Justice Leveson is expected to report back within a year.

Live video of all the sessions is being streamed on the inquiry's website