Leigh Daynes, spokesman for the British Red Cross, said the charity was "extremely concerned" about the breach of confidentiality, which is an essential condition of its access to detention centres across the world.
But the committee has decided that trying to investigate where the leak came from would be a waste of time.
Ian Piper, spokesman for the committee, said: "The feeling here is that it would be a hiding to nothing. We gave the report to the coalition forces in February, what they did with it afterwards we have no knowledge of or control over.
"It is the first time in more than 20 years that such a report has been leaked. Even people at the Red Cross who are reasonably senior don't get to see these reports - they really are kept under wraps. That, and the fact that it was leaked to the Wall Street Journal, rather than a paper in Europe, means we are confident that (the US) is where it originated from."
As guardians of the Geneva Convention and, therefore, of the 'rules of war', the Red Cross is the only organisation granted access to prisons throughout the world to monitor the way inmates are treated. It is allowed to interview prisoners without witnesses, and reports verbally on those interviews to prison authorities afterwards. More comprehensive written reports, such as the one that was leaked, are published after several visits.
Daynes defended the ICRC's decision not to make its Iraq report public.
"Last year, the ICRC visited almost 500,000 prisoners in 80 countries and we cannot jeopardise that. Our primary concern is to protect the life and dignity of detainees and we don't necessarily believe it is in their best interests for their evidence to be made public. They have ongoing protection needs and we don't want to endanger their situation."
Last week, Prime Minister Tony Blair offered the Red Cross the opportunity to set up permanent offices at British-controlled prisons in Iraq - a significant concession which goes beyond the requirements of the Geneva Convention.