The former US defence secretary, Donald Rumsfeld, admits in his memoirs that he made a mistake in claiming that Saddam Hussein had weapons of mass destruction sites round Baghdad and Tikrit, one of the main justifications for launching the Iraq invasion.

Rumsfeld says now: "I made a misstatement." What he meant to say is there were 'suspect sites'.

The incident is one of many in the 815-page autobiography, Known and Unknown, in which he seeks to revise the history of the Bush administration on issues ranging from Iraq to the Guantánamo detention centre.

Rumsfeld is one of the most controversial figures of the Bush era and his autobiography has long been awaited. The Guardian obtained an advance copy.

He recounts how during the Iraq invasion in 2003 he was asked on a news programme about WMD. He says he normally tried to be reserved and precise on intelligence matters but in this instance he made a mistake. "Recalling the CIA's designation of various 'suspect' WMD sites in Iraq, I replied: 'We know where they are. They're in the area around Tikrit and Baghdad.' My words have been quoted many times by critics of the war as an example of how the Bush administration misled the public."

Critics of the war, he writes, accused the Bush administration of lying, compiling "a small string of comments – ill-chosen or otherwise deficient – to try to depict the administration as purposefully misrepresenting the intelligence."

But, Rumsfeld says: "While I made a few misstatements – in particular the one mentioned above – they were not common and certainly not characteristic. Other senior administration officials also did a reasonably good job of representing the intelligence community's assessments accurately in their public comments about Iraqi WMD, despite some occasionally imperfect formulations."

As well as the "misstatement" on WMDs, he expresses regret over one of his most famous comments about Iraq: "stuff happens". He was speaking about looting of the museum in Baghdad in the immediate aftermath of the invasion, and the phrase later became the title of a play. Rumsfeld was criticised for failure to send enough troops to Iraq to maintain security.

He said he been speaking at a Pentagon press briefing when "I vented some annoyance by uttering a few ill-chosen words". The phrase "stuff happens" sounded callous. He says he had been thinking about the riots that followed the assassination of Martin Luther King.

"I had uttered more than 1,000 words at that press conference before I said 'stuff happens' but they were the only two words that seemed to matter", he says.

He condemns the media coverage for overblowing the extent of the looting and then failing to report as prominently that in fact only a small portion of Iraq's treasures were looted.

Rumsfeld oversaw the setting up of Guantánamo and says that tough interrogation techniques were necessary at the time for use on those with time-sensitive information that could save US lives. But he had not authorised waterboarding, which is simulated drowning.

"I did not believe it would be appropriate for anyone in defence department custody to be waterboarded or stripped and subjected to cold temperatures, and I rejected these techniques," he writes.

The techniques he did approve were intended for use with one key individual only, Mohammed al-Qahtani, the Saudi taken to Guantánamo in 2002 who was accused of trying to enter the US to join the 9/11 hijackers but being refused entry.

"Qahtani provided useful information about al-Qaida's planning for 9/11, its methods of cross-border infiltration, and information about bin Laden's bodyguards," he writes.

Rumsfeld says that two-and-a-half years later he had learned what happened during his interrogation. "I was surprised and troubled. Some of what took place sounded to me as if the interrogation plan may have gone beyond the techniques I approved."

Qahtani was apparently exposed to cold temperatures, stripped and humiliated, Rumsfeld says. The techniques "may not have been in keeping with the intent of my January 2002 order that all detainees in the custody of the defence department were to be treated humanely".

He criticises Barack Obama for hounding the Bush administration over Guantánamo but having failed to close it himself, and, in fact, kept in place many of the Bush administration policies.

He also cites the increased use by Obama of drones in Afghanistan and Pakistan. "It is worth noting that killing these individuals by drone missile attacks affords them fewer legal rights than the military commissions President Obama opposed for years," Rumsfeld says.