The paper is thought to be offering settlements to at least eight people whose voicemail was listened to.
But a lawyer for the actress Sienna Miller said she was continuing her legal action.
Mark Lewis, representing the publicist Nicola Phillips, said his client had turned down an offer from the paper.
The NoW printed its apology in its latest edition over the long-running phone-hacking scandal.
The paper said of the victims: "Here today, we publicly and unreservedly apologise to all such individuals."
It added in a page two article that the hacking "should not have happened" and "was and remains unacceptable".
The NoW's owner, News International, has admitted there were at least eight victims and has put aside £20m for compensation.'Fairly and efficiently'
The paper said a number of individuals had brought breach of privacy claims against it over wrongful "voicemail interceptions" between 2004 and 2006, and others were threatening to do so.
Lawyer Charlotte Harris, who is involved in several of the current cases, said the NoW's apology was "limited" and several unanswered questions remained.
She told BBC Radio 5 live: "It's all very well saying 'okay, fine, we admit that happened', but how are we meant to know the extent of what happened?
"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 need to be answered, and they can only be answered if we carry on with the cases and don't just settle them in one go."
Ms Harris, whose clients include football agent Sky Andrew and actress Leslie Ash, also said since the apology, people previously frightened to take action would be encouraged to come forward.
The NoW's apology stated: "Evidence has recently come to light which supports some of these claims.
"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."Sienna Miller's lawyer says she has not accepted any offer of settlement
The BBC understands that News International is ready to settle claims over phone hacking with eight people including Sienna Miller, former Culture Secretary Tessa Jowell, designer Kelly Hoppen and sports broadcaster Andy Gray.
The others are Mrs Jowell's estranged husband, lawyer David Mills; former aide to ex-Deputy Prime Minister Lord Prescott Joan Hammell; Nicola Phillips, assistant to publicist Max Clifford; and former Olympian and talent agent Sky Andrew.
Ms Miller's lawyer Mark Thomson said she had not accepted any offer of settlement from the NoW over phone-hacking.
He said: "Sienna's claims are based on outrageous violations of her privacy. Her primary concern is to discover the whole truth and for all those responsible to be held to account."Court claims
On Friday, News International apologised over the phone-hacking scandal and said it would set up a compensation fund.
There are 24 active claims against the paper being heard by High Court judge Mr Justice Vos.
Mark Lewis, a solicitor involved in several of the current cases, told the BBC that News International's apology was a "step in the right direction".
In 2007, the first police investigation led to the convictions and imprisonment of then NoW royal editor Clive Goodman and private investigator Glenn Mulcaire, who was employed by the paper.
On Tuesday, the NoW's chief reporter Neville Thurlbeck, 50, and former news editor Ian Edmondson, 42, were arrested on suspicion of having unlawfully intercepted voicemail messages. They were subsequently released on bail until September.
News International - which is owned by Rupert Murdoch and also owns the Times and the Sun newspapers - said it would continue to co-operate with the Metropolitan Police inquiry.
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