The ICRC has said the US was aware of reports that its officials had showed disrespect towards Islam's holy book at the Guantanamo Bay detention centre.
Newsweek's report triggered anti-US rallies in the Muslim world
The comments come days after US weekly Newsweek retracted a report about desecration of the Koran at the centre.
The ICRC gave no details of the nature of the disrespectful incidents it said it reported "multiple times" to the US.
The Pentagon confirmed that the ICRC had approached "on rare occasion" with allegations from detainees.
Pentagon spokesman Bryan Whitman said log entries from Guantanamo had included incidents such as a Koran falling to the floor by accident.
Washington has endeavoured to quell anger in the Muslim world after the publication of Newsweek's article, which sparked violent protests. It said "lasting damage" had been done to its image.
At least 15 people were killed in anti-US riots on Afghanistan.
The International Committee of the Red Cross said it had reported the allegations in confidence to Pentagon officials many times in 2002 and 2003.
ICRC spokesman Simon Schorno said he believed the US had acted on the information.
"The US government took corrective measures and those allegations have not resurfaced," Mr Schorno said.
On Monday, Newsweek said its report that interrogators at Guantanamo Bay had flushed a copy of the Koran down a toilet was based on flawed sources.
As well as the deaths in Afghanistan, more than 100 people were injured in violent protests across the Muslim world, from Pakistan to Indonesia, following the initial publication.
Insulting the Koran or the Prophet Muhammad is regarded as blasphemy and punishable by death in both Pakistan and Afghanistan.
The White House said it was now Newsweek's obligation to help reverse the effects of its report.
Newsweek's original story claimed that a military investigation was set to reveal evidence of desecration of the Koran at Guantanamo.
It followed repeated allegations by former prisoners at the camp in Cuba that interrogators had prevented them from worshipping or had sought ways to insult their faith.
But on 16 May, the magazine said the investigation in question had not looked at the desecration charges, and that its sources had also backed away from the story.