The allegation is the most serious so far to have emerged from the police investigation into illegal phone hacking at the Rupert Murdoch-owned newspaper.
Police were today meet with executives at the newspaper after Milly Dowler's distraught parents demanded legal action. The police investigation has been widely criticised.
Bob and Sally Dowler condemned the News of the World as ‘heinous’ and ‘despicable’.
If the claims are substantiated senior executives at the paper could face police charges.
Prime Minister David Cameron said today: “If they [the claims] are true this is a totally dreadful act in a totally dreadful situation.”
Amanda "Milly" Dowler was an English teenager who was abducted on her way home from school at the age of 13 in Walton-on-Thames, Surrey, on 21 March 2002, and subsequently murdered.
Her body was discovered on 18 September 2002.
On 23 June 2011, Levi Bellfield was found guilty of Dowler's murder and sentenced to a whole-life prison tariff.
But, according to the Dowlers' lawyer Mark Lewis, the News of the World hacked into Milly's voicemail after she went missing, even deleting some messages to make room for more to arrive.
This could have interfered with the police investigation and raised false hopes Milly was still alive and using the phone, he added.
The allegations are the latest twist in a phone hacking scandal that has engulfed the Rupert Murdoch-owned title, which is the biggest Sunday paper in the world.
Rebekah Brooks – who is now the UK chief executive at the News of the World’s parent company, News International – was editor at the newspaper when Milly was snatched. She has already said she will not be resigning over the matter and has Mr Murdoch's full support.
Mr Lewis said: “It is distress heaped upon tragedy to learn the News of the World had no humanity at such a terrible time.
“The fact they were prepared to act in such a heinous way that could have jeopardised the investigation and give them false hope is despicable.”
News of the World executives were working through the night prior to meeting with police at 9am Tuesday.
Scotland Yard refused to comment, but a senior police source told the Daily Telegraph: “This was a gross, gross breach of journalistic standards. Really terrible. We are only just beginning to see the scale of what was going on.”