Fifteen people died and scores were injured in violence between protesters and security forces, prompting US promises to investigate the allegations.
"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," Newsweek editor Mark Whitaker wrote in a note to readers.
In an issue dated May 9, the magazine reported that US military investigators had found evidence that interrogators placed copies of Islam's holy book in washrooms and had flushed one down the toilet to get inmates to talk.
Whitaker wrote that the magazine's information came from "a knowledgeable US government source," and before publishing the item, writers Michael Isikoff and John Barry sought comment from two Defense Department officials.
One declined to respond, and the other challenged another part of the story but did not dispute the Quran charge, Whitaker said.
But on Friday, a top Pentagon spokesman told the magazine that a review of the military's investigation concluded "it was never meant to look into charges of Quran desecration. The spokesman also said the Pentagon had investigated other desecration charges by detainees and found them `not credible.'"
Also, Whitaker added, the magazine's original source later said he could not be sure he read about the alleged Koran incident in the report Newsweek cited, and that it might have been in another document.
"Top administration officials have promised to continue looking into the charges, and so will we," Whitaker wrote.
Newsweek Washington Bureau chief Daniel Klaidman said the magazine believes it erred in reporting the allegation that a prison guard tried to flush the Quran down a toilet and that military investigators had confirmed the accusation.
"The issue here is to get the truth out, to acknowledge as quickly as possible what happened, and that's what we're trying to do," Klaidman told the CBS Evening News on Sunday.
Following the report, demonstrations spread across Afghanistan, and Islamic leaders gathered to pass a resolution calling for anyone found to have abused the Quran to be punished.
Many of the 520 inmates at Guantanamo are Muslims arrested during the US-led war against the Taliban and its al-Qaeda allies in Afghanistan.
US National Security Adviser Stephen Hadley said in an interview for CNN's Late Edition that the allegations were being investigated "vigorously."
"If it turns out to be true, obviously we will take action against those responsible," he said.