The government was told of allegations UK troops abused Iraqi prisoners a year ago, Amnesty International has said.
Mr Hoon is unlikely to reveal the Red Cross report's contents
The group said it warned last May that prisoners had been tortured and one killed.
It comes after Downing Street confirmed it had received a Red Cross report on abuse concerns in February.
Amid mounting pressure to reveal when the government knew of the claims, Defence Secretary Geoff Hoon has promised to make a statement to the Commons on Iraq on Monday.
Now Amnesty says it first raised allegations of torture and the death of one Iraqi in UK custody in a memo to the Ministry of Defence last year.
This was followed by meetings with government officials.
It met Ministry of Defence and Foreign Office officials last June to which the government responded two weeks later with a letter.
Amnesty says it sent another memo detailing allegations of mistreatment of prisoners in July and wrote again to Mr Hoon in October.
The government replied that month promising an investigation, the group said.
The MoD was unable to confirm details of the correspondence.
An Amnesty spokesman said it had hoped for an "impartial and civilian-led inquiry" but instead the claims were investigated by the "secretive" Royal Military Police.
"Torture and ill-treatment is entirely unacceptable and there must be a full
and independent inquiry as a matter of urgency," the spokesman added.
Amnesty said Mr Blair and Mr Hoon would have been sent thousands of letters in January about the death of an Iraqi prisoner from its members.
The government is already being called upon to reveal the contents of a Red Cross report it received in February about alleged abuse.
This was three months before the Daily Mirror published photographs allegedly showing prisoners being maltreated by British troops.
And on Friday it emerged the Red Cross had also warned US officials of alleged abuses involving American troops more than a year ago.
'Leaked in US'
The MoD has said it is "not likely" to publish the confidential Red Cross document.
A spokesman said action had been taken in response but declined to give details.
Shadow defence secretary Nicholas Soames said: "It appears Amnesty warned the government last May that there was a problem in a very small number of cases of mistreatment of prisoners." .
He said the Red Cross document had been leaked in the USA which made it difficult to argue against releasing it in Britain.
Earlier former Foreign Secretary Robin Cook said it was important the government made public the Red Cross report's contents.
And Liberal Democrat leader Charles Kennedy told BBC One's Politics Show the government should publish whatever evidence it may have been given by the Red Cross.
"People have a right to know. We have got to get to the bottom of this. It is very, very serious indeed," he said.