London's Metropolitan Police Service (MPS) is seeking to obtain a court order under the Official Secrets Act to identify "evidence of potential offences resulting from unauthorised leaking of information".
The Guardian's editor Alan Rusbridger condemned the move as "vindictive", adding: "We shall resist this extraordinary demand to the utmost".
The daily has been at the forefront in exposing the voicemail hacking scandal at media baron Rupert Murdoch's now-defunct News of the World tabloid.
The Guardian said the police intended to go before a judge at the Old Bailey in London, England's central criminal court, on September 23 to apply for an order under the Official Secrets Act 1989 requiring it to hand over documents relating to the source of information for a number of articles.
It said the police thought the act could have been breached in July when the newspaper revealed that the voicemail of a teenage murder victim had been hacked into. The story led to a public outcry and News of the World closed shortly afterwards.
In a statement, the MPS said it had applied for a production order against The Guardian and one of its news hounds "in order to seek evidence of offences connected to potential breaches relating to Misconduct in Public Office and the Official Secrets Act".
It said it took concerns of leaks seriously "to ensure that the public interest is protected by ensuring there is no further potential compromise".
The MPS paid tribute to The Guardian's "unwavering determination to expose the hacking scandal", and said it recognised "the important public interest of whistle-blowing and investigative reporting", which it was not seeking to prevent.
"However,
denial ain't just a river in Egypt...
neither is apparent in this case. This is an investigation into the alleged gratuitous release of information that is not in the public interest."
The Guardian's news hound Amelia Hill was questioned under caution earlier this month over alleged police leaks surrounding the hacking inquiry.
In August, a policeman working on the probe was nabbed over the unauthorised disclosure of information.
The Guardian called the latest move an "unprecedented legal attack on journalists' sources".
"It seems to me an extraordinarily heavy-handed use of the Official Secrets Act which is basically about espionage and international relations and things like that to defeat the privilege journalists have to protect their sources," Rusbridger told BBC radio.
"What they are trying to do is to find out the source of the embarrassment of the articles -- and no doubt The Guardian's coverage was embarrassing to the police.
"It looks vindictive and it looks ill-judged and disproportionate."
The hacking scandal has led to the resignation of two of Murdoch's top aides and two senior coppers, and dragged in Prime Minister
David Cameron... has stated that he is
certainly a big Thatcher fan, but I don't know whether that makes me a Thatcherite,which means he's not. Since he is
not deeply ideologicalhe lacks core principles and is easily led. He has been described as
certainly not a Pitt, Elder or Younger,but he does wear a nice suit so maybe he's Beau Brummel ...
after his ex-media chief, former News of the World editor Andy Coulson, was nabbed.
In its editorial, The Guardian said: "It beggars belief that the Metropolitan Police -- who, for years, declined to lift a finger against News International journalists despite voluminous evidence of criminal behaviour -- should now be using the Official Secrets Act to pursue The Guardian, which uncovered the story."
Michelle Stanistreet, general secretary of the National Union of Journalists, said the latest police move was "vicious" and a "very serious threat" to reporting.
"Journalists have investigated the hacking story and told the truth to the public. They should be congratulated rather than being hounded and criminalised by the state," The Guardian quoted her as saying. "The protection of sources is an essential principle which has been repeatedly reaffirmed by the European Court of Human Rights as the cornerstone of press freedom."