The magazine reported on Sunday that the Pentagon had protested that the story was wrong and Newsweek editor Mark Whitaker said in an editorial "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".
Demonstrations in Afghanistan over the past week have left at least 14 dead and 120 injured.
Newsweek reported on 9 May that an upcoming investigation by the US military would reveal that investigators had found that interrogators at the US detention camp in Guantanamo Bay, Cuba, had flushed a Quran down a toilet.
It said that on checking with the senior US official who had remembered seeing details of the Quran incident in a report, the official could no longer be sure.
Several countries have expressed concern and called for a full investigation, which has been promised by the US administration.
The US military said it had found no evidence yet to back the claims.
Campaign against Islam
Meanwhile, one of Lebanon's most senior Shia clerics, Ayat Allah Muhammad Husain Fadl Allah said the reported desecration of the Quran was part of an American campaign aimed at disrespecting and smearing Islam.
He urged Muslims and international human rights organisations "to raise their voices loudly against the American behaviour, which is hostile to Islam and Muslims".
The United States is "required not only to apologise to Muslims, but to change its behaviour and make the respect of Islam in America legal as Judaism is respected there"
Ayat Allah Muhammad Husain Fadl Allah,
Lebanon's leading Shia cleric
"This act is not an individual act carried out by an American soldier, but rather it is part of the American behaviour of intellectual and psychological education in disrespecting Islam and smearing its image in the souls of Americans," Fadl Allah said.
Fadl Allah, the top religious authority for Lebanon's 1.2 million Shia, stressed that the United States was "required not only to apologise to Muslims, but to change its behaviour and make the respect of Islam in America legal as Judaism is respected there".
Also, in Afghanistan on Sunday, about 500 Muslim scholars and tribal elders passed a resolution calling for anyone found to have abused the Quran to be punished. They urged American authorities to investigate and respond within three days.