The News of the World has publicly apologised to victims of the newspaper's phone-hacking controversy, saying that the invasions of privacy "should not have happened".
In a statement printed in today's newspaper, the paper said it wanted to "unreservedly apologise" to celebrities whose telephone messages were intercepted.
Under the heading "Voicemail interception: An apology" on page two of the newspaper, it said "a number of individuals" had brought breach of privacy claims against it and that yet more were planning to do so.
"Evidence has recently come to light which supports some of these claims," the News of the World said.
"We have written to relevant individuals to admit liability in these civil cases and to apologise unreservedly, and will do the same to any other individuals where evidence shows their claims to be justifiable.
"We hope to be able to pay appropriate compensation to all these individuals, and have asked our lawyers to set up a compensation scheme to deal with genuine claims fairly and efficiently.
"Here today, we publicly and unreservedly apologise to all such individuals.
"What happened to them should not have happened. It was and remains unacceptable."
The apology was accompanied by a News International statement, in which it said "past behaviour" at the newspaper was "a matter of genuine regret".
It comes as one of the victims, actress Sienna Miller, vowed to do everything possible to hold to account those responsible for the "outrageous violations of her privacy".
The star's solicitor Mark Thomson released a statement on her behalf which read: "Sienna's claims are based on outrageous violations of her privacy; her voice mails were persistently hacked and the information obtained was used to publish numerous intrusive articles over a period of a year.
"She is awaiting information and disclosure from the News of the World which has been ordered by the court and will consider her next steps once this is provided.
"Her primary concern is to discover the whole truth and for all those responsible to be held to account."
Mr Thomson said Miller had not accepted any offer of settlement and the News of World had not submitted to judgment in her claim and the action was continuing.
It is understood that along with Miller, the company has issued apologies to former Culture Secretary Tessa Jowell, her estranged husband lawyer David Mills and footballer turned broadcaster Andy Gray.
Football agent Sky Andrew, publicist Nicola Phillips and Joan Hammell, a former special adviser to Lord Prescott, are also believed to have received apologies through their solicitors.
News International said the move applied to allegations of voicemail hacking at the News of the World from 2004 to 2006.
Designer Kelly Hoppen is also understood to have been issued with an apology, although only for that time period, and not for a later claim.
No one else is understood to have received an apology - other notable figures who have pursued the matter through the courts, including Leslie Ash and Lord Prescott, are not thought to be covered by the admissions.
Condemnation of the paper's actions has gathered pace with former MP George Galloway, who said he had been shown proof that his phone had been hacked, claiming the News of the World apology was a "cynical attempt to protect the company's chief executive Rebekah Wade".
And Labour leader Ed Miliband demanded to know who knew about the "criminal behaviour", and when.
He said: "What we have seen is a serious admission of wrongdoing by News International.
"We have now got to get to the bottom of any criminal behaviour, which is a matter for the police and should be thoroughly investigated.
"We need to know who knew about these actions and when.
"We also need to know how far across the organisation knowledge of these actions went."
The controversy has been a source of continuing embarrassment for News International at a time when its parent group, Rupert Murdoch's News Corporation, has been seeking to take full control of BSkyB.
Earlier this week detectives investigating the allegations arrested the paper's chief reporter and its former head of news.
Neville Thurlbeck, 50, and Ian Edmondson, 42, were held by Scotland Yard detectives on Tuesday when they voluntarily attended separate police stations in south-west London.
The paper's former editor Andy Coulson resigned as Prime Minister David Cameron's director of communications in January as he said that the continuing row about the affair was making his job impossible.
Days later the Met launched a fresh investigation, codenamed Operation Weeting, after receiving "significant new information" from News International.
Cabinet minister Danny Alexander described the hacking as "a very serious scandal", adding that the court cases and police investigation "must go forward".
"It's outrageous that people have had their voicemails hacked into, seemingly a large number of people," the Chief Secretary to the Treasury told BBC1's Andrew Marr Show.
"That's not something that could be acceptable in any set of circumstances."
But he said the hacking would not have any bearing on News Corporation's attempts to take over BSkyB.
"The decision about BSkyB and News Corp is something which is being considered completely separately," Mr Alexander said.
Shadow Welsh Secretary Peter Hain insisted the police must pursue the allegations "to the end".
"There are more revelations coming out by the day, and it's vital that there is a full and proper public investigation on this," he said.
"It's vital that the police pursue it to the end - frankly they've been tardy up until recent times, they've not really identified the truth or brought criminal prosecutions where they are necessary."
He added: "Who knows what they were up to really? This is a really serious media scandal."
Mayor of London Boris Johnson said all newspaper editors should declare whether they know of any phone hacking activities by their own staff.
"An investigation is going on, plainly the police need to get on with it," he told Sky News' Murnaghan programme.
"But what I would like to see is the entire newspaper industry - what we used to call Fleet Street - have a general truth and reconciliation commission about all this. That's what we need to have.
"I think all the editors and all the proprietors should come forward, put their hands up, and say whether they know of any of their reporters or employees who may or may not have been into these practices which have been exposed at the News of the World.
"I think that would be a very healthy development."