Colin Powell has fired back at Dick Cheney for what the former secretary of state calls "cheap shots" directed at him and other members of the Bush administration in the former vice president's new book.

"In My Time: A Personal and Political Memoir," gives Cheney's account of the eight-year administration of President George W. Bush. Powell, a retired four-star Army general, served as Bush's secretary of state until January 2005.

Powell complained Sunday to Bob Schieffer, host of CBS' "Face the Nation," that in the book, Cheney takes credit for Powell's resignation and suggests that Powell wasn't supportive of Bush's positions.

"Well, who went to the United Nations and, regrettably, with a lot of false information?" Powell asked, referring to his 2003 visit to the U.N. Security Council in which famously said there was "no doubt" that then-Iraqi leader Saddam Hussein was working to build nuclear weapons. "It was me. That wasn't Mr. Cheney."

Powell also blasted Cheney's account of the Valerie Plame affair, in which covert CIA operative Plame's name was leaked to the media after her husband, Joe Wilson, publicly questioned the rationale for going to war with Iraq.

Cheney "tries to lay it all off on Mr. Rich Armitage and the State Department and me," Powell said.

Cheney and Powell may have served in the same administration, but their relationship has soured over the years. The two have been trading jabs on the Sunday talk shows for some time.

"The new president is going to have to fix the reputation that we've left with the rest of the world," Powell said in October 2008 on NBC's "Meet the Press" when he was asked to reflect on having once declared that Cheney was "one of the most distinguished and dedicated public servants this nation has ever had."

"I didn't know he was still a Republican," Cheney said of Powell during a May 2009 appearance on "Face the Nation."

Cheney told NBC News last week that there will be "heads exploding all over Washington" when his tell-all memoir hits stores Tuesday.

"That's quite a visual," Powell said in the Sunday interview with Schieffer. "And in fact, it's the kind of headline I would expect to come out of a gossip columnist or the kind of headline you might see one of the supermarket tabloids write. It's not the kind of headline I would have expected to come from a former vice president of the United States of America."

Powell also criticized Cheney for using "an almost condescending tone" in the book when he described Condoleezza Rice as "tearful." Rice succeeded Powell as secretary of state.

"There's nothing wrong with saying you disagree, but it's not necessary to take these kinds of barbs and then try to pump a book up by saying heads will be exploding," Powell said. "I think it's a bit too far. I think Dick overshot the runway with that kind of comment."

In the NBC interview, Cheney defended the description.

"She was tearful," he told NBC's Jamie Gangel. "That's what I wrote. If I wanted to say she was crying, I would have said she was crying. ... It is an accurate description of what happened and what I saw."