The remarks came in a video posted online in reaction to a new Senate report revealing the real scope of a Bush-era interrogation program.
Kenneth Roth, executive director of the group, said Obama's reluctance to look into the rendition, detention and interrogation program meant that some future president facing a security threat may look at torture as a policy option.
Despite banning the intelligence agency’s detention and interrogation program, Obama made clear immediately after assuming office in 2009 that he was opposed to a full inquiry into former President George W. Bush’s administration programs such as treatment of terror suspects, saying that "we need to look forward as opposed to looking backwards."
"By choosing to move on, to forget about the past, not to prosecute this serious crime, Obama is keeping torture as a misguided wrongful policy option for some future American president," Roth said.
"It’s not too late to change that, Obama still has two more years [in office]," he said.
The 500-page document issued Tuesday by the Senate Intelligence Committee is an unclassified executive summary of a 6,700-page report that remains classified.
The more than five-year investigation into the CIA’s interrogation practices from late 2001 to early 2009 found techniques were ineffective in obtaining accurate information or detainee cooperation. It also said lawmakers and the White House were misled by the agency about the effectiveness and the extent of the brutality of the techniques.
The report cited methods that employed the use of nudity; waterboarding – which it said induces convulsions and vomiting; sleep deprivation for as long as 180 hours; and unnecessary “rectal hydration.”
Roth also criticized the CIA for relying on the legal opinions of Bush administration lawyers, calling them "twisted efforts to justify the unjustifiable."
"Every soldier in war knows that you should never follow an illegal order, and we should expect no less from the CIA," he said.
The American Civil Liberties Union also released a statement urging a federal investigation into those responsible for the torture program.
"Now that we have additional evidence of the wrongs committed in our name, we must demand accountability. We’re calling on Attorney General Eric Holder to appoint a special prosecutor to conduct an independent investigation of the torture program," said Anthony D. Romero, the group’s executive director.
"Impunity for torture is indefensible," he added.