"No, I don't," he told David Axelrod on "The Axe Files," a podcast from the University of Chicago Institute of Politics and CNN.
McCain said he found "appalling" Trump's assertion in an interview earlier this year that the US lacked the moral standing to question Russian President Vladimir Putin's human rights abuses. "We've got a lot of killers.
What do you think, our country's so innocent?" Trump said at the time.
"To state that there's some moral equivalency between an imperfect nation -- that's the United States of America -- and Vladimir Putin is appalling," McCain responded.
"And I think it's pretty clear that there's a difference between, well, aren't we killers and the guy that stood there and said, 'Mr. Gorbachev, take down this wall,'" he said, recalling Reagan's historic challenge to Soviet leader Mikhail Gorbachev delivered in a 1987 speech at the Berlin Wall.
In contrast to Trump's posture toward Russia, Reagan "spoke out for the captive nations" under Soviet rule and gave hope to the citizens there, McCain said. "That's a pretty big difference."
By assaulting a foundational principle of American democracy, McCain said, Russia's interference in the 2016 presidential election
was an act more destructive than if the US had been attacked through conventional warfare.
"It's one thing to destroy a building with a bomb or inflict damage, but if you destroy the fundamentals of a free and open society, which is what democracy is all about, you inflict incredibly heavier damage," he said.
The White House did not immediately return a request Saturday for comment on McCain's remarks.
Multiple congressional investigations and an FBI probe are underway to determine if there was any collusion between figures associated with the Trump campaign and the Russian efforts to influence the 2016 election.
But McCain was cautious when asked if he would consider any contacts between Americans and the Russians who interfered with the election to be an act of treason.
"There's one thing to have a conversation. It's another thing to plot together," he said. "But I think it would be something that that individual would have to be held accountable."
During this conversation, which also aired on CNN Saturday night, McCain, the chairman of the Senate Armed Services Committee, expressed concerns about the philosophical gulf between Trump's national security team and key members of his White House staff.
Registering his strong support for Defense Secretary James Mattis; Lt. General H.R. McMaster, Trump's national security adviser; and John F. Kelly, the Homeland Security secretary, McCain called the group "the strongest (national security team) I've seen."
But the Arizona senator said their appreciation for global institutions and America's leadership role stood in contrast with the views of his chief strategist, Steve Bannon, and policy director Stephen Miller, who are seen as the architects of Trump's neo-isolationist, "America First" rhetoric.
"I know that the President has great respect for these former military people that he has given the most important national security posts," McCain said. Yet, he added, "Everybody tells me that Mr. Bannon has his ear constantly. So there is a contradiction within this administration."
The President's foreign policy team must navigate their internal divisions while at the same time confronting "a world in incredible turmoil," McCain said. The 2008 Republican presidential nominee, who ran against Barack Obama, ascribed much of that turmoil to Obama's policies, which he termed an "unmitigated disaster."
"I am more worried about this country than I've been in my entire lifetime," he said. "We are seeing strains on the world order."
To hear the whole conversation with McCain, click on http://podcast.cnn.com
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