LONDON – The News of the World publicly apologised on Sunday for hacking into the voicemail of numerous top celebrities, in a scandal that has engulfed top politicians, royals and stars.

As it sought to draw a line under the furore, the Rupert Murdoch-owned weekly tabloid said sorry to its victims, saying its actions had been "unacceptable".

The Sunday paper said it had admitted liability in some cases and planned to pay compensation from a fund being set up, reportedly worth around £20 million.

However, several victims seem unlikely to accept the compensation offer, preferring instead to get the full extent of the phone-hacking revealed in open court.

Referring to the victims, the News of the World said: "We publicly and unreservedly apologise to all such individuals.

"What happened to them should not have happened. It was and remains unacceptable," added the paper, in the article printed on page two, headlined "Voicemail interception: An apology".

The News of the World's public statement came after the paper's owner, News International, said sorry for phone hacking on Friday.

In Sunday's apology, the paper said that some people had taken action against the paper for breach of privacy over "wrongful voicemail interception" between 2004 and 2006, and others were threatening to do so.

"Evidence has recently come to light which supports some of these claims," it said.

"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," it added.

Actress Sienna Miller is believed to be among those offered settlements from the compensation fund.

But Miller shows little sign of dropping her ongoing legal action.

Her lawyer Mark Thomson insisted the star's "primary concern is to discover the whole truth and for all those responsible to be held to account."

Lawyer Charlotte Harris, who is involved in several of the cases, said the apology left several unanswered questions.

"It's all very well saying 'okay, fine, we admit that happened', but how are we meant to know the extent of what happened?", she told BBC radio.

"It's not just about money. We want to know who was it you listened to, who else was involved, how far up, exactly what period, what else have you got, why weren't we told?

"These questions... can only be answered if we carry on with the cases."

As well as Miller, former Cabinet minister Tessa Jowell and sports commentator Andy Gray are reported to be among those offered pay-offs.

Treasury Secretary Danny Alexander described the hacking as "outrageous" and "a very serious scandal", adding that the court cases and police investigation "must go forward".

London Mayor Boris Johnson said the entire newsper industry should have a "truth and reconciliation commission".

"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," he told Sky News television.

The News of the World's apology capped a turbulent week for the paper.

On Tuesday, its chief reporter Neville Thurlbeck and a former news editor Ian Edmondson were arrested on suspicion of having unlawfully intercepted mobile phone voicemail messages.

The controversy has dogged the paper for the past few years.

In 2007, the initial police investigation led to the News of the World's royal correspondent Clive Goodman and a private investigator being jailed.

They had hacked into the mobile phone messages of Princes William and Harry to obtain information for use in stories.

A steady stream of fresh allegations and criticism of the original probe prompted London's Metropolitan Police to reopen their investigation in January.

That move came days after the tabloid's former editor, Andy Coulson, quit as head of communications for Prime Minister David Cameron.

Coulson had resigned as editor when Goodman was jailed but insisted he knew nothing of the phone hacking. He continues to deny wrongdoing, but said the continuing scandal was distracting him from his job with Cameron.