Arizona Sen. John McCain "sometimes" regrets his vote for Secretary of State Rex Tillerson, especially in the wake of Tillerson floating the idea that the United States has been taking the wrong approach in Syria.

McCain said on CBS Sunday said his vote in favor of Tillerson pains him on occasion, and comments Tillerson said made about the conflicting plans of the United States and Russia in Syria, which McCain saw as kowtowing to the Kremlin, are troubling.

"Sometimes I do," McCain said when asked if he regrets voting for Tillerson. "But, I'm still torn by the fact that the American people chose this president and he ought to be able to have this team."

McCain said Tillerson does not appear to believe in the same American ideals that he does and that the Republican Party stood for under President Ronald Reagan.

He said the Russians know what they're doing by backing the Syrians, and they know about Bashar Assad's more vile tactics such as using chemical weapons.

He said Tillerson's statement that the United States may have the wrong approach is divorced from American ideals.

"He is divorced from a fundamental of American democracy. The reason we are the shining city on the hill as Ronald Reagan used to say, is because of our principles," he said.

McCain added, "I know what the slaughter has been like. I know that the Russians knew Bashar Assad was going to use chemical weapons. And to say maybe we've got the wrong approach?"

President Trump and his foreign policy team are in danger of upending the post-World War II global order that has been in place for more than 70 years. Trump's tweet Sunday morning proposing a cybersecurity partnership with the Russians is an example of the administration not taking Russian President Vladimir Putin seriously.

"There has to be a price to pay … otherwise he will be encouraged to do so again," he said. "Does anyone doubt [Putin's] intentions of undermining American supremacy?"

He added, "I am sure that Vladimir Putin could be of enormous assistance in that [cybersecurity] effort because he's doing the hacking."