McCain noted that he and Cheney always had strong disagreements, especially on Cheney's torture policies, the Washington Post reported.
Cheney said on a Sunday talk show he believed having Palin as McCain's running mate in the 2008 presidential election was a mistake.
McCain told Fox News he was proud of his former presidential running mate while bringing up Cheney's support of torturing detainees.
"I'm always glad to get comments four years later," McCain said on the Fox Web site.
"Look, I respect the vice president. He and I had strong disagreements as to whether we should torture people or not. I don't think we should have."
"But the fact is that I'm proud of Sarah Palin, I'm proud of the job she did, I'm proud of the job she continues to do, and so everybody has their own views and I respect those views, but I'm proud of what we did," McCain added.
Many Republican strategists have been critical of Palin. But Cheney's daughter, Liz, said on Twitter she has huge respect for Palin.
Notable deaths of 2014 [PHOTOS]