Senior members of the Bush administration who approved the use of waterboarding and other harsh interrogation measures could face prosecution, Barack Obama said today, in a surprise about-turn by the president.

He said his attorney general, Eric Holder, was conducting an investigation and the final decision rested with him.

Obama cited four Bush administration memos he released last week detailing CIA interrogation measures, saying they "reflected, in my view, us losing our moral bearings".

The revelation of possible prosecutions amounts to a turnaround by Obama, who had been resisting a prolonged and divisive partisan row that could distract from his heavy domestic and foreign agenda.

He also lifted his opposition to a separate congressional inquiry today.

The White House press secretary, Robert Gibbs, said the president would like to see the inquiry modelled on the 9/11 commission.

Obama reiterated that there would be no prosecutions 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 he opened up the possibility that those in the Bush administration who gave the go-ahead for the use of waterboarding and other interrogation techniques could be prosecuted.

"For those who carried out some of these operations within the four corners of legal opinions or guidance that had been provided from the White House, I do not think it's appropriate for them to be prosecuted," Obama said. "With respect to those who formulated those legal decisions, I would say that that is going to be more of a decision for the attorney general within the parameters of various laws, and I don't want to prejudge that."

He did not name any individuals. Those in the frame could be George Bush's attorney general, Alberto Gonzales, or, lower down the chain, justice department lawyers.

The White House chief of staff, Rahm Emanuel, said only three days ago that the administration did not favour prosecutions of those who had devised the policy, and Gibbs echoed that on Monday.

Obama's about-turn may reflect the sense of outrage, at least among US liberals, over further details of CIA interrogations that have emerged during the last few days, including the use of waterboarding against one detainee 183 times. Or it could be purely political, a retaliation for sniping against him by Cheney.

In an interview with Fox News on Monday night, Cheney said he was disturbed by the release of the previously classified memos. He called for the declassification of other memos that he said would illustrate the value of intelligence gained from the interrogations.

"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," he said.

Earlier this year, momentum had been building among Democrats in Congress for a commission to look into Guantánamo and the CIA's secret sites. But that began to fizzle out when the Obama White House indicated it was opposed to the idea.

Obama again today indicated he remained opposed to politicisation of the issue, saying it might hamper national security operations.

But, in a switch, he said: "If and when there needs to be a further accounting of what took place during this period, I think for Congress to examine ways that it can be done in a bipartisan fashion ... that would probably be a more sensible approach to take.

"I'm not suggesting that that should be done, but ... I think it's very important for the American people to feel as if this is not being dealt with to provide one side or another political advantage, but rather is being done to learn some lessons so that we move forward in an effective way."

Prominent in any inquiry will be the authors of the four memos setting out the legal basis for the interrogation methods, Jay Bybee, assistant attorney general under Bush, and Steven Bradbury, principal deputy assistant attorney general.

It is not just Cheney who has been sniping at Obama over Guantánamo and interrogation.

Marc Thiessen, a former Pentagon and White House official, criticised the president for releasing the memos. "President Obama's decision to release these documents is one of the most dangerous and irresponsible acts ever by an American president during a time of war - and Americans may die as a result."