In an interview with Fox News, the president suggested he thinks the US and Russia are as bad as each other.
When asked by Bill O'Reilly if he respects Mr Putin, Mr Trump replied: "I do respect him."
Asked to elaborate, he added: "Well, I respect a lot of people but that doesn't mean I'm going to get along with him. He's a leader of his country. I say it's better to get along with Russia than not.
"And if Russia helps us in the fight against Isis, which is a major fight, and Islamic terrorism all over the world, that's a good thing.
"Will I get along with him? I have no idea."
Mr O'Reilly then said: "But he's a killer though. Putin's a killer."
Mr Trump replied: "There are a lot of killers. We've got a lot of killers.
"What do you think, our country's so innocent?"
Mr Trump has said he is prepared to review the sanctions imposed on Russia over its annexation of Ukraine's Crimea Peninsula in 2014.
Senator John McCain, who chairs the Senate Armed Services Committee, spoke out against a possible move by the White House to lift sanctions against Russia.
He called the Russian leader "a murderer and a thug" and said he "seeks to undermine American national security interests at every turn."
When Mr Trump spoke to Mr Putin over the phone, the first time he had spoken directly with the Russian leader, the pair reportedly did not hacking in the US election or the lifting of sanctions.
During the full interview, due to be broadcast on Fox before the Super Bowl, Mr Trump also answered a question about his unverified allegations of voter fraud.
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