"The fact of the matter is, he encouraged me to give him my view on a whole range of issues. I did," Cheney said in an interview broadcast on "Fox News Sunday."
"Sometimes he agreed. Sometimes he did not. That was true from the very beginning of the administration," Cheney said.
Among their disagreements: Cheney supported taking military action against Iran's nuclear program. Mr. Bush, however, wanted to try engaging Iranian leaders first.
"It was not my decision to make," Cheney said. "The president made the decision and, obviously, we pursued the diplomatic avenues."
Earlier reports cast Mr. Bush and Cheney at opposite ends on several other issues. Cheney reportedly disagreed with Bush's decision to stop waterboarding terror suspects - a harsh interrogation tactic that critics call torture. He also reportedly differed with the president on whether to pursue diplomatic talks with North Korea.
On the flip side, Cheney reportedly agreed with Bush on closing secret prisons where interrogators have greater latitude to question terror suspects than at the U.S. Navy base at Guantanamo Bay.
Asked directly about each, Cheney punted.
Does he feel Mr. Bush was less tough on foreign policy during his second term in office than in his first?
"I wouldn't say that," Cheney told Fox News.
Cheney also said the Obama administration shouldn't be driven by a deadline to leave Iraq if the country isn't stable enough by then to remain secure.
"I think there's a danger there that you're going to let the drive to get out overwhelm the good sense of staying long enough to make certain the outcome is what we want," he said.
However, the deadlines in the U.S. security agreement with Iraq - which calls for all American combat troops to leave by the end of 2011 - was negotiated by the Bush administration.
In the end, being a consummate Washington power player, Cheney plugged his upcoming book to provide the answers about where he butted heads with Mr. Bush.
"I think you are going to have wait and read my book," he said.