"I think Susan Rice is tainted. She rolled out on five Sunday talk shows with the message of the administration that this was a violent response to a video and nothing was further from the truth, we know that it was an act of terror," said Duncan on "Fox and Friends."
Duncan made the remarks after he was asked if McCain's comments meant he was changing his own stance on Rice.
"I think she deserves the ability and the opportunity to explain herself and her position," McCain said on "Fox News Sunday."
He added that President Obama was the problem, not Rice.
Rice was accused of misleading the public after she appeared on numerous talk shows to brief the press on the deadly Sept. 11 attacks on the U.S. mission in Benghazi, Libya.
Last week, 97 House Republicans sent a letter to the president calling Rice's credibility into question and opposing efforts to nominate her to the top diplomat position. Obama has not announced any nomination, but Rice is seen as a front-runner to be nominated to replace Clinton, who is planning to step down from her position early in Obama's second term.
The Senate would vote to confirm Rice, making any Senate opposition to her nomination important. The House has no role in confirming Cabinet positions, though the comments of lawmakers like Duncan could raise the pressure on Republican senators to oppose a Rice nomination.
Duncan also directed blame at the White House.
"The real question here is why was Susan Rice put on the Sunday talk shows with a message that misled the American people about the real reason behind the attacks in Benghazi, especially when it was just weeks before a very important presidential election," he said.
When pressed on whether he could be persuaded to reverse his decision after further questioning of Rice, Duncan said that it's an issue of "credibility."
"Do we want someone as secretary of State that is somehow tainted in this whole Benghazi issue? I don't think so ... whether it's intentional or unintentional, she is tainted in this issue," Duncan said.