Scotland Yard has "decided not to pursue" its legal bid to force the Guardian to reveal the sources it used for stories about phone hacking.
A hearing was scheduled for Friday but police said they had consulted the Crown Prosecution Service and opted "at this time" not to go ahead with it.
The CPS said it had asked for more information and more time.
Guardian editor Alan Rusbridger said the paper welcomed the Met's decision "to withdraw this ill-judged order".
'Not targeting journalists'
The Met has been looking into allegations of leaks to the Guardian newspaper by an officer from Operation Weeting, which is investigating hacking by the News of the World.
Last month, an unnamed 51-year-old detective constable was arrested and bailed until 29 September, pending further inquiries. He has been suspended from work.
Under the Police and Criminal Evidence Act, the Met had applied for a production order against the Guardian newspaper and one of its reporters.
It also said it was investigating whether an officer from Operation Weeting may have breached the Official Secrets Act by passing on information.
But, after consulting the Crown Prosecution Service on Monday and taking further legal advice on Tuesday, the Met says it has decided not to proceed against the newspaper.
The newspaper, however, has accused the police of trying to use the Official Secrets Act to force it to identify its sources for stories about murdered girl Milly Dowler's phone being hacked by the tabloid.
In a statement, Scotland Yard denied there was any intention to "target journalists or disregard journalists' obligations to protect their sources".
It said: "This decision [to drop the legal bid] does not mean that the investigation has been concluded.
"This investigation, led by the DPS [Directorate of Professional Standards] - not Operation Weeting - has always been about establishing whether a police officer has leaked information, and gathering any evidence that proves or disproves that."
The Met's Deputy Assistant Commissioner Mark Simmons defended its "robust" investigation into the leaks.
He told BBC Radio 4's Today programme: "We've acknowledged and I've acknowledged the role the Guardian has played in the history of what brought us to where we are now, both in terms of its focus on phone hacking itself and indeed its focus on the Met's response to that.
"But in all the glare that has been thrown on to our relationships with the media, we have had to ask ourselves the question about how do we do more to ensure that public confidence in our officers treating information given to them in confidence appropriately is maintained."
He added that there had been difficulties finding a "new balance" in the Met's relationship with the media following recent revelations.
Editor Mr Rusbridger acknowledged Mr Simmonds' remarks but cautioned against moves to curb responsible journalism.
"I just hope that in our effort to clean up some of the worst practices we don't completely overreact and try and clamp down on perfectly normal and applaudable reporting," he said.
"This was a regrettable incident, but let's hope it's over."
Earlier, Mr Rusbridger said: "Threatening reporters with the Official Secrets Act was a sinister new device to get round the protection of journalists' confidential sources.
"We would have fought this assault on public interest journalism all the way. We're happy that good sense has prevailed."
The National Union of Journalists also criticised the use of the Official Secrets Act by the police, with the union's General Secretary Michelle Stanistreet describing it as "flagrant abuse".
"This was an outrageous attack on a central tenet of journalism - the protection of our sources. This is a victory for journalism, democracy and press freedom," she said.
The Crown Prosecution Service and Met Police said they would work jointly in considering the next step.
The Guardian's report in July about Milly Dowler's phone being hacked re-ignited the phone-hacking scandal, leading to the News of the World's closure.
News International, publisher of the News of the World, is understood to be close to a £3m compensation deal with the Dowler family, which could include a £1m donation to charity.