In a letter to MPs, the force insisted that it had not handed the newspaper any messages from the teenager's mobile phone after she went missing on March 21, 2002.
Allegations that the News of the World hacked into Dowler's phone have played a pivotal role in the phone hacking scandal that resulted in the paper's closure last July.
Surrey Police has confirmed that the News of the World called the force in April 2002 to claim that it had a recording obtained by accessing the schoolgirl's voicemail.
The 16-page letter, published by the Commons culture, media and sport select committee, details the conversations between Surrey police and the News of the World.
It sets out how an unnamed journalist from the paper contacted the force around a month after Dowler disappeared, claiming to reveal information relating to a specific voicemail left by a recruitment company on her phone.
The message appeared to suggest that Dowler had registered with the agency, but police later found out that it was left in error and was meant for somebody else.
At the time, the police insisted to the reporter that the message was most likely from a hoaxer claiming to be the missing schoolgirl, but the journalist responded by saying that the News of the World "had got Milly's phone number and PIN from school children".
Intent on getting a scoop, the News of the World had sent "hordes of reporters" to the agency in the north of England, including some claiming to be co-operating with Surrey Police, which the letter notes was "untrue".
The article claimed that police were "intrigued" by the alleged new lead, but after complaints from the force, it was modified in later editions to suggest that the call was a hoax.
The agency had actually rung Dowler's number by mistake, and left a message for "Nana", which the journalists had wrongly deduced as "Amanda", Milly's proper name.
In the letter, the force says: "The information [in the voicemail] was not provided to the NOTW by Surrey Police.
"The NOTW obtained that information by accessing Milly Dowler's voicemail. The message [referred to by the NOTW journalist] was left after Surrey Police had last [legally] accessed Milly Dowler's voicemail."
> Fresh Milly Dowler phone hacking details emerge
The reporter also told police that other voicemail messages on Dowler's phone included one from a "tearful relative", a young boy and someone saying "It's America, take it or leave it".
The culture committee chairman, Tory MP John Whittingdale, told Sky News that it appears as the News of the World journalists "may have actually interfered or impeded the police in their investigations".
Surrey Police has been criticised over its decision not to launch an investigation at the time after the newspaper confirmed that it had heard Dowler's voicemails.
The letter to MPs does not say why the force did not investigate the paper, and it also does not shed any more light on what happened to the voicemails, or who was responsible for deleting some of them, which gave the 13-year-old's parents false hope that she was still alive.
The Guardian claimed last July that the News of the World had hacked Dowler's phone and deleted some messages in the first few days after her disappearance.
But after fresh inquiries by the Metropolitan police, it emerged that while the tabloid did hack the voicemails, it was unlikely that it was behind the deletions. The Met police is still investigating this and has not yet reached any conclusions.