Meanwhile, Defence Secretary Geoff Hoon would come under pressure on Monday to explain exactly what and when the government knew about allegations that British troops abused Iraqi prisoners.
"We apologise deeply to anyone who has been mistreated by any of our soldiers," Blair told French television during a visit to Paris.
"That is absolutely and totally unacceptable. Those who are responsible for this, if they have behaved in this appalling way, they will be punished according to the army discipline and rules."
However he added: "The activities of a few people who have brought shame to their situation should not detract from the work done by the vast majority."
As the government acknowledged it had known for months about claims that its troops abused Iraqi prisoners, lawmakers called for the publication of an International Committee of the Red Cross report detailing many of the allegations.
Human rights group Amnesty International said it told British officials about reports of violence and torture a year ago.
Amnesty says it has been documenting "patterns of torture" by occupation troops in Iraq for more than a year.
Amnesty said it first warned UK
government of abuse last May
The human rights group said on Sunday it first warned the government last May that prisoners had been tortured, and at least one killed, in British custody.
The group said it had held a series of meetings with Foreign Office and defence ministry officials over the past year.
"They said they would look into it and get back to us," said Amnesty's Middle East spokeswoman, Nicole Choueiry. "Since then, they did not get back to us."
The Ministry of Defence could not confirm when it was first told of the allegations. But a spokeswoman said the ministry had been "investigating cases of alleged abuse since way back into last year." The ministry is investigating 33 cases in all, she said.
The Red Cross also has said it warned American officials of prisoner abuse in Iraq more than a year ago.
On Saturday, Blair's office said they had been shown the Red Cross report in February. Officials would not discuss its contents.
"I find it intolerable that all we know about this report is what has actually leaked in Washington," former foreign secretary Robin Cook told the BBC's Breakfast with Frost programme.
Cook, who resigned from Blair's Cabinet last year to protest against the war in Iraq, said publishing the report was the only way to "see what independent people are saying about the problem and how severe it is".
Cook's call for publication was supported by Conservative Party co-chairman Liam Fox and Liberal Democrat foreign affairs spokesman Sir Menzies Campbell.
"Only total transparency and swift investigation will provide answers ... It is not only the integrity of the army which is at stake but the safety of those serving in Iraq"
Sir Menzies Campbell,
Liberal Democrat foreign
"Only total transparency and swift investigation will provide answers," Campbell said. "It is not only the integrity of the army which is at stake but the safety of those serving in Iraq."
The Ministry of Defence said Hoon would make a statement to the House of Commons on Monday about the allegations of abuse.
However, a spokeswoman said the government was unlikely to publish the confidential Red Cross report.
On Friday, the Wall Street Journal published details from the report describing beatings and humiliation of prisoners at Baghdad's Abu Ghraib prison and in the British-controlled southern city of Basra.
Roland Huguenin-Benjamin, a spokesman for the Red Cross, said on Sunday the organisation identified concerns with every prison camp in Iraq.
"The concern we have been expressing for a year now deals with a general pattern of mistreatment of detainees," he told Sky television. "What we are tackling in our reports is the overall treatment of prisoners in general in camps under coalition forces in Iraq.
"We were warning of the fact that the treatment given to prisoners and in particular the way they were prepared for interrogation is not acceptable from the point of view of the Geneva Convention."