Cheney, who has a long history of heart disease, said concern about a possible health crisis was one of the main reasons he kept the letter. Former President George W Bush knew about it and so did a Cheney staff member.
"I did it because I was concerned ... for a couple of reasons," Cheney said.
"One was my own health situation. The possibility that I might have a heart attack or a stroke that would be incapacitating. And, there is no mechanism for getting rid of a Vice President who can't function."
Cheney, who spoke to NBC about his forthcoming memoir "In My Time," gave a few glimpses of some of the book's topics and said it was likely to be controversial.
"There are going be heads exploding all over Washington," he said.
Within the Bush administration, Cheney was one of the staunchest advocates of so-called "enhanced" interrogations of terrorism suspects, such as waterboarding and sleep deprivation.
He said in the interview he had no regrets about his stance on such tactics and said he would "strongly support" the United States using waterboarding again "if we had a high value detainee and that was the only way we could get him to talk."
While Cheney has repeatedly insisted that waterboarding and similar techniques yielded valuable information from militants, numerous top intelligence and law enforcement officials dispute that contention. Moreover, they said techniques that many equate with torture yielded false confessions that sent US officials on wild goose chases.
Cheney, along with key aides, was also a proponent of the 2003 U.S.-led invasion of Iraq, which the Bush administration justified by citing weapons of mass destruction and al Qaeda ties that dictator Saddam Hussein turned out not to possess. Days before the invasion, Cheney predicted US troops would be "greeted as liberators."
In the interview, which will air on August 29, NBC's Jamie Gangel pressed Cheney on differences he had with Bush on Iraq and cited one example in which the former president cleared all of the aides out of his office and asked Cheney: "Dick, what do you think we should do?"
Gangel asked Cheney whether the book might embarrass Bush with its revelations of private conversations that highlighted the sway the vice president held in decision-making.
"I didn't set out to embarrass the president or not embarrass the president," Cheney said. "If you look at the book there are many places in it where I say some very fine things about George Bush. And believe every word of it."
Cheney's book is due out on August 30.
Washington: Former vice president Dick Cheney signed a secret resignation letter shortly after taking office in 2001 and kept it in a safe, according to an excerpt of an NBC interview released on Wednesday.
First Published: Thursday, August 25, 2011, 16:10