"John's entitled to his opinion. I just think he's wrong," said Cheney, a friend of Rumsfeld. He also disclosed that the Arizona senator had apologized to him for a previous comment that the vice president had "badly served" President Bush on Iraq.
"John said some nasty things about me the other day, and then next time he saw me, ran over to me and apologized. Maybe he'll apologize to Rumsfeld," Cheney said in an interview with ABC News.
McCain's campaign declined to comment on Cheney's remarks.
Despite having low job approval numbers overall, the vice president continues to be very popular among rank-and-file Republicans, and many of them are likely to vote in next year's GOP presidential caucuses and primaries.
McCain, who lost the Republican nomination to Bush in 2000, is expected to formally announce his second run for the White House next month. He faces strong challenges from Mitt Romney, the former Massachusetts governor, and Rudy Giuliani, the ex-mayor of New York.
On the campaign trail this week, McCain has talked at length with voters about Iraq and defended his staunch support of Bush's 21,500-troop buildup there while criticizing the way the war has been handled.
"We are paying a very heavy price for the mismanagement — that's the kindest word I can give you — of Donald Rumsfeld, of this war," McCain said in Hilton Head Island, S.C., on Monday. "The price is very, very heavy and I regret it enormously."
"I think that Donald Rumsfeld will go down in history as one of the worst secretaries of defense in history," McCain added.
Rumsfeld stepped down last year after a rocky six-year tenure.
A former defense secretary himself, Cheney was asked about McCain's comments while on the USS Kitty Hawk at the Yokosuka Naval Base in Japan. He called Rumsfeld a great secretary.
"I know a little bit about the job. I've watched what he's done over there for six years. I think he did a superb job in terms of managing the Pentagon under extraordinarily difficult circumstances," Cheney said. "He and John McCain had a number of dustups over policy, didn't have anything to do with Iraq."
Last month, McCain blamed both Cheney and Rumsfeld for a "terribly mishandled" war.
"The president listened too much to the vice president . . . Of course, the president bears the ultimate responsibility, but he was very badly served by both the vice president and, most of all, the secretary of defense," McCain was quoted as telling The Politico, a Capitol Hill newspaper and Web site.
A few days later, Cheney said, McCain approached him on the Senate floor, said he had been quoted out of context and offered an apology.
"I was happy to accept," Cheney said.