Senior members of the Bush administration who approved the use of waterboarding and other harsh interrogation measures could face prosecution, President Obama disclosed today .

He said the use of torture reflected America "losing our moral bearings".

He said his attorney general, Eric Holder, was conducting an investigation and the decision rested with him. Obama last week ruled out prosecution of CIA agents who carried out the interrogation of suspected al-Qaida members at Guantánamo and secret prisons around the world.

But for the first time today he opened up the possibility that those in the administration who gave the go-ahead for the use of waterboarding could be prosecuted.

The revelation will enrage senior Bush administration figures such as the former vice-president Dick Cheney.

The Obama administration views the use of waterboarding as torture, while Cheney claims it is not.

Obama, taking questions from the press during a visit by King Abdullah of Jordan, reiterated he did not believe in prosecution of those CIA agents who carried out the interrogations within the guidelines set down for them. But "with respect to those who formulated'' the policies, "that is going to be more of a decision for the attorney general within the parameters of various laws". He added: "I don't want to prejudge that."

He also opened the way for a Congressional inquiry into the issue.

Meanwhile the former US vice-president Dick Cheney has called for the disclosure of CIA memos which reveal the "success" of torture techniques, including waterboarding, used on al-Qaida suspects under the Bush administration.

Cheney said that, according to secret documents he has seen, the interrogation techniques, which the Obama administration now accepts amounted to torture, delivered "good" intelligence. He hinted that it had significant consequences for US security.

Cheney was speaking out in response to the release by Barack Obama of four Bush administration memos detailing the agency's interrogation methods used against al-Qaida suspects.

"One of the things that I find a little bit disturbing about this recent disclosure is they put out the legal memos, the memos that the CIA got from the Office of Legal Counsel, but they didn't put out the memos that showed the success of the effort," Cheney said in an appearance on Fox News.

"I haven't talked about it, but I know specifically of reports that I read, that I saw, that lay out what we learned through the interrogation process and what the consequences were for the country.

"I've now formally asked the CIA to take steps to declassify those memos so the American people have a chance to see what we obtained and what we learned and how good the intelligence was."

Obama yesterday visited CIA headquarters to defend the publication of the internal documents. The row gathered further momentum yesterday when it emerged that one detainee, Khalid Sheikh Mohammed, had been subjected to waterboarding 183 times and another, Abu Zubaydah, 83 times.

Obama is keen to try to put the row behind him, reluctant to see prosecutions that could be politically divisive and distract attention from his heavy domestic and foreign agenda.

In a speech to about 1,000 staff aimed at restoring CIA morale, Obama, who promised last week that CIA operatives would not be prosecuted, reiterated that he would stand by them.

"Don't be discouraged by what's happened in the last few weeks," Obama said. "Don't be discouraged that we have to acknowledge potentially we've made some mistakes. That's how we learn."

At a private meeting with 50 rank-and-file CIA members at their headquarters in Langley, Virginia, before his speech, Obama heard "understandable anxiety and concern" from agents fearful of prosecution.

The CIA's director during the Bush administration, Michael Hayden, who criticised the release of the memos, warned on Sunday that agents could be vulnerable because of the memos, facing civil lawsuits or congressional inquiries.

Sensitive details were blacked out in the memos seen by most of the media on Thursday but over the weekend Marcy Wheeler, of the Emptywheel blog, found a copy in which crucial details were not masked.

That copy showed that Mohammed had been subjected to waterboarding – which simulates drowning – 183 times in March 2003. He had been arrested in Pakistan at the start of that month. Abu Zubaydah, a Saudi captured in Pakistan in March 2002, was subjected to waterboarding 83 times in August 2002.

Mohammed had admitted to involvement in terrorist actions before his capture but, after being interrogated, confessed to a list of incidents and plots that included the 1993 attack on the World Trade Centre in New York, as well as a plot to attack Heathrow, Big Ben and Canary Wharf, the beheading of the US journalist Daniel Pearl, and the Bali bombing.

Abu Zubaydah denied involvement with al-Qaida.

Obama, defending himself against those in the CIA who argued that he should not have released the memos, said legally he had no grounds for blocking a freedom of information request from the US human rights group, the American Civil Liberties Union.

"I acted primarily because of the exceptional circumstances that surrounded these memos, particularly the fact that so much of the information was public," Obama said.

Standing in front of a wall with 89 stars, each depicting an officer killed in action, Obama praised the CIA as the "tip of the spear" in protecting the US from its enemies.

Obama said he understood that intelligence officials must sometimes feel that they are working with one hand tied behind their backs. But, rebutting Hayden, he said: "What makes the United States special and what makes you special is precisely the fact that we are willing to uphold our values and our ideals even when it's hard, not just when it's easy, even when we are afraid and under threat, not just when its expedient to do so.

"So yes, you've got a harder job and so do I, and that's OK. And over the long term, that is why I believe we will defeat our enemies, because we're on the better side of history."

Hayden had argued that the harsher interrogation techniques had provided valuable information and said that the techniques did not amount to torture.

Human rights lawyers question the credibility of the confessions because they were obtained under duress.

The White House press secretary Robert Gibbs, when asked yesterday why Bush administration lawyers could not be prosecuted, said: "The president is focusing on looking forward."