The White House emphatically resisted those calls Wednesday in the wake of the landmark report on Bush-era practices, the first thorough public account of how the agency delivered punishment at secret sites around the world, imprisoned some suspects unfairly, and allegedly misled elected officials about the program.
In the face of this can of worms, the White House appeared more determined to slam it shut than further sift its contents.
Josh Earnest, a spokesman for President Barack Obama, repeatedly changed the subject when asked substantive questions like: Did the torture achieve anything? Will anyone be punished?
Indeed, Earnest responded to those questions and others with the same vague expression of regret that the CIA practices had hurt America's moral standing in the world.
"One of the most powerful tools in our arsenal to protect and advance our interests around the globe is the moral authority of the United States of America," he said.
In fact, over the course of Wednesday's news conference, Earnest repeated the words "moral authority" 31 times.
"The commander-in-chief concluded that the use of the techniques ... described in this report significantly undermine the moral authority of the United States of America. And that's why the president, on his second full day here at the White House, issued an executive order ending those tactics."
As for whether there might be charges, Earnest said the Justice Department had already conducted a review.
In 2009, Obama's attorney general instructed a longtime prosecutor to study the issue and found no grounds to lay charges. The department said this week that it stands by its decision, which was reached after a thorough investigation.
Civil-liberties groups want more. They want charges, either in the U.S. or abroad, or at least a presidential pardon for a handful of people involved in the CIA program — if only to make the symbolic point that the practices were illegal.
The United Nations also waded in.
The UN's high commissioner on human rights noted that the report coincided with the 30th anniversary of the UN Convention Against Torture, and he applauded the U.S. and Brazil this week for issuing reports on past abuses.
But he called for more.
"The convention lets no one off the hook — neither the torturers themselves, nor the policy-makers, nor the public officials who define the policy or give the orders," said high commissioner Zeid Ra'ad Al Hussein, a member of the Jordanian royal family.
"If someone commits murder, they are prosecuted and jailed. If they commit rape or armed robbery, they are prosecuted and jailed. If they order, enable or commit torture — recognized as a serious international crime — they cannot simply be granted impunity because of political expediency."
The issue is relevant in Canada, said Kerry Pither, the author of a book about four Canadians imprisoned abroad, including Maher Arar.
There have been no consequences for members of Canada's security apparatus who co-operated with American intelligence, said Pither. She cited the example of Michel Cabana, the supervisor in charge of the RCMP investigation targeting those four men, who has since been promoted to deputy commissioner of the Mounties.
As for compensation, Arar reached a $10-million settlement with the Canadian government but the others are still fighting the government in court.
"I was appalled," Pither said of the government's description of the torture report as an American issue.
"There is no doubt — we know from the findings of (the Arar and Iacobucci) inquiries that Canadian agencies were working closely with the CIA. Rather than put our hands up and saying 'No' to torture, we co-operated. We delivered Canadians into the hands of the torturers who were carrying out the dirty work."
At the White House briefing, Earnest was also pressed about the ongoing U.S. drone program, and asked how the president can call it un-American to torture people when he personally administers a program that bombs civilian areas.
One of the architects of the CIA program made that same point, suggesting in an interview that what Obama's now doing is worse.
"To me it seems completely insensible that slapping (9-11 mastermind) Khalid Sheikh Muhammad is bad but sending a Hellfire missile into a family's picnic and killing all their children, and killing granny, and killing everyone, is OK," former military psychologist James Mitchell told Vice News.
"One of the reasons is, what about all that collateral loss of life? The other one is, if you kill them you can't question them."
Mitchell's role has been previously identified in news reports — which he doesn't deny but won't discuss.
The Senate report refers to him through a pseudonym, describing how he and a partner helped set up the interrogation program, then created a private company that received more than $80 million to help run it.