Panetta was quoted in a profile in New Yorker magazine as saying Cheney "smells some (political) blood in the water on the national security issue," and "It's almost as if (Cheney) is wishing that that this country would be attacked again in order to make his point," Politico reported.
The White House refused to be drawn into the controversy, Politico reported, but U.S. Sen. John McCain, R-Ariz., backed Cheney.
"Mr. Panetta should retract, and retract immediately," McCain said on Monday's "Fox and Friends."
In a statement provided to The Hill, Cheney said, "I hope my old friend Leon was misquoted ... The important thing is whether or not the Obama administration will continue the policies that have kept us safe for the last eight years."
Cheney has been a critic of the Obama administration's policies, saying they make the country less safe.