Mr Cheney said that the decision to publish the memos was a mistake.
And it was misleading, he said, because the documents did not include those demonstrating that harsh interrogation delivered intelligence "success".
"One of the things that I find a little bit disturbing about this recent disclosure is that they put out the legal memos... but they didn't put out the memos that show the success of the effort," Mr Cheney told Fox News.
"There are reports that show specifically what we gained as a result of this activity. They have not been declassified. I formally ask that they be declassified now."
The American people should have a chance to weigh the intelligence obtained alongside the legal debate, he said.
Mr Cheney made his comments as US President Barack Obama visited the CIA headquarters just outside Washington.
If we're going to release the documents on the torture policy, it makes sense to release the documents that would be pertinent in evaluating the policy made by the Bush administration, if such documents do exist (that is a big if). Evidence suggests that Bush's "harsh interrogation" policy was not effective, so probably documents don't exist Up till now, Bush administration officials have assured us that "harsh interrogation methods" are effective, but they have shown no evidence. Perhaps Cheney knows no documents of this description exist, but is calling for their release to make it appear that Obama is with-holding these documents for political reasons.
Even if they exist, it would be hard to determine whether the torture is in fact an effective method. Even if Khalid Sheikh Muhammed broke under the 183 water-boardings he received, there's no way of knowing that another tact wouldn't have worked just as effectively.
My opinion: take up Cheney's challenge, and declassify as many documents as we can on the results of our torture policy. Whatever these documents show, it is better to have fuller transparency on what occurred.