He told the FBI the US had "used the 9/11 attack as a justification" to invade Iraq.
The details were among more than 100 pages of notes written by Piro after Saddam was found hiding in a "spider-hole" on a farm near Tikrit, his home town.
Piro wrote that Saddam "believed Iran intended to annex southern Iraq", and that the perceived threat "was the major factor as to why he did not allow the return of UN inspectors to verify destruction of the weapons".
Saddam fought a ruinous, eight-year war with Iran from 1980, during which Iraq used chemical weapons.
But he told the FBI that Iraq had destroyed all of its chemical and biological weapons long before the US invasion, and even said he considered seeking a security agreement with Washington as a protection against Iran.
The US and UK governments largely justified their invasion of Iraq on the belief that Saddam had weapons of mass destruction and could readily deploy them.
The former Iraqi leader denied having unconventional weapons before the US invasion, but refused to allow UN inspectors to search his country from 1998 until 2002.
"By God, if I had such weapons, I would have used them in the fight against the United States," he told Piro.
During the interviews, Saddam also denied reports that he used body doubles, saying the claim was "movie magic, not reality".
He could only remember using the telephone twice since March 1990, and said he communicated mainly through couriers.
Saddam was executed in December 2006 after being convicted of crimes against humanity by an Iraqi court for the killing of 148 Shia men and boys following a 1982 assassination attempt.