"I think his assessment is off the mark," Cheney wrote in an opinion piece in the Wall Street Journal.
In his new book, "The Age of Turbulence: Adventures in a New World," Greenspan criticized President George W. Bush for the emergence of big deficits after he came to office in 2001 following the surpluses of the Clinton administration.
The former Fed chief said he urged Bush to veto a string of "budget busting" and "out-of-control" spending bills, but to no avail.
Greenspan, a Republican, echoed some other members of his party in saying that spending on initiatives such as a prescription drug benefit were unrealistic when the administration also had pushed through big tax cuts.
But Cheney, a longtime friend of Greenspan from their service during Gerald Ford's presidency, blamed the 2001 recession and the aftermath of the September 11 attacks for the growth in red ink and noted that over the past couple of years, the deficits have decreased.
Cheney said Bush had "pressed hard" to limit the growth in spending outside of the military and homeland security.
"Alan credits me in his book for my 'intensity' and 'sphinxlike calm' -- and it's in a spirit of friendship that I offer him these gentle reminders of the Bush record," Cheney said.
Greenspan has come under criticism of his own both for endorsing Bush's 2001 tax cuts and failing to air his criticisms in public earlier.