In a statement released today News International said it has decided to approach some civil litigants with an "unreserved apology and an admission of liability in cases meeting specific criteria".
News International said it has instructed lawyers to establish a compensation scheme to begin the process of bringing these cases to a "fair resolution" with damages "appropriate to the extent of the intrusion".
It is understood that the number of cases News International is willing to concede liability on is fewer than 10 but that as the company is currently working through the cases this could rise.
News International said it would continue to contest cases that it believes are without merit or where it is not responsible but a spokeswoman for News International could not confirm how many cases it intended to fight.
News of the World royal correspondent Clive Goodman and private investigator Glenn Mulcaire, who was paid £100,000 a year by the tabloid, were sent to prison for intercepting messages of royal aides in January 2007.
The hacking had come to light after the News of the World ran a story about Prince William pulling a tendon in his knee, something few people knew about, in 2005. News International, however, always insisted it was the work of a "rogue reporter".
Despite News International’s insistence that phone-hacking was not known to senior managers and was an isolated incident, the News of the World’s then editor Andy Coulson quit over the affair in 2007, taking responsibility for the incident while maintaining he had no knowledge of the practise of phone-hacking at the paper.
Broadsheet newspaper The Guardian began its campaign to unravel the "rogue reporter" defence in July 2009 when it revealed that News International had made payments worth a combined £1m to settle cases involving three people.
One of the three, Gordon Taylor, the former professional footballer and chief executive of the Professional Footballer’s Association, was paid £700,000 in legal costs and damages to prevent him speaking out about the case.
By 2009 Coulson was employed by the Conservative Party as its director of communications, a role he took to Number 10 when the coalition government was formed in May 2010. Coulson was forced to quit his government role as the phone-hacking story gathered momentum.
Many high profile figures have said they believe their phones were hacked including former deputy prime minister John Prescott and Sienna Miller, named by the Guardian today as one of those who will be offered a settlement.
There are currently tens of cases against News International being brought by individuals who believe their messages were intercepted by News Int staff.
Scotland Yard reopened its investigation into the affair following the long-running campaign in the Guardian. The investigation is ongoing and a number of arrests of News of the World staff have been made since new evidence came to light.
On Wednesday, Lord Prescott, the former Labour deputy prime minister, called for the decision over whether to allow News Corp, News Int's parent company, to take full control of broadcaster BSkyB to be delayed until after the phone-hacking inquiry had been concluded.
The News International statement in full
News International statement with regard to voicemail interception at the News of the World during 2004-2006.
Following an extensive internal investigation and disclosures through civil legal cases, News International has decided to approach some civil litigants with an unreserved apology and an admission of liability in cases meeting specific criteria.
We have also asked our lawyers to establish a compensation scheme with a view to dealing with justifiable claims fairly and efficiently.
This will begin the process of bringing these cases to a fair resolution with damages appropriate to the extent of the intrusion.
We will, however, continue to contest cases that we believe are without merit or where we are not responsible.
That said, past behaviour at the News of the World in relation to voicemail interception is a matter of genuine regret. It is now apparent that our previous inquiries failed to uncover important evidence and we acknowledge our actions then were not sufficiently robust.
We continue to co-operate fully with the Metropolitan Police. It was our discovery and voluntary disclosure of this evidence in January that led to the re-opening of the police investigation.
With that investigation on going, we cannot comment further until its completion.
News International's commitment to our readers and pride in our award-winning journalism remains undiminished.
We will continue to engage with and challenge those who attempt to restrict our industry’s freedom to undertake responsible investigative reporting in the public interest.