The US news weekly has apologised for mistakes in a story, which said that interrogators at Guantanamo Bay had violated the Koran.
The report two weeks ago sparked outrage and led to demonstrations in Muslim countries. In Afghanistan, the protests turned deadly and 15 people died and many more were injured.
Newsweek editor Mark Whitaker said: "We regret that we got any part of our story wrong, and extend our sympathies to victims of the violence and to the US soldiers caught in its midst."
The May 9 edition of the magazine reported that US military personnel had placed copies of the Islamic holy book in bathrooms and flushed at least one copy down the toilet as part of a strategy to get Guantanamo Bay detainees to talk.
Newsweek said the story had come from "a knowledgeable US government source". The writers of the piece, Michael Isikoff and John Barry, had asked US Defence Department officials for comment and there was no response on the Koran allegation.
However, on Friday the Pentagon said that it found the desecration charges "not credible".
"Certainly the fact that the Pentagon and the top Pentagon spokespeople are denying it and saying we got the story wrong troubles us. This is all we've been able to find out. We suggest we may have gotten something wrong, but we're not entirely sure what we got wrong at this point, frankly," Whitaker told The Wall Street Journal.
In the editor's letter, Whitaker apologised for the violence it caused in the Middle East and said that the magazine regretted that it got any part of its story wrong. It extended its sympathies to victims of the violence and to the US soldiers caught up in the trouble.
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