WASHINGTON (CNN) -- Vice President Dick Cheney said Wednesday he "fundamentally" disagreed with John McCain's recent criticism of former Defense Secretary Donald Rumsfeld, and suggested the Arizona senator may owe the former secretary of defense an apology.

"I just fundamentally disagree with John," Cheney told ABC News regarding McCain's comment Monday contending "Rumsfeld will go down in history as one of the worst secretaries of defense in history."

McCain, a frontrunner for the GOP presidential nomination, made the comment while campaigning in Florida.

"I think Don [was] a great secretary," Cheney added. "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 also said McCain recently apologized to him for telling "The Politico" last month that President Bush "listened too much to the vice president" and "was very badly served by both the vice president and, most of all, the secretary of defense."

The vice president said the Arizona Republican came up to him on the Senate floor a few days later, "said he'd been quoted out of context and then basically offered an apology, which I was happy to accept."

"John said some nasty things about me the other day, and then next time he saw me, ran over to me and apologized," Cheney said. "Maybe he'll apologize to Rumsfeld."