Trump made the remarks to Fox News' Bill O'Reilly in an interview that will air before the Super Bowl. Excerpts of the interview were released Saturday, NBC News reported.
When O'Reilly asked why Trump respects Putin the president said, "Well, I respect a lot of people but that doesn't mean I'm going to get along with him."
When O'Reilly made the claim that "Putin's a killer," Trump responded: "There are a lot of killers. We've got a lot of killers. What, do you think our country's so innocent?"
US intelligence agencies have accused Russia of being involved in alleged cyber-attacks on US Democratic Party institutions during the presidential election.
Trump resisted those claims but in January acknowledged that Russia was involved. He said the cyber-attacks had no effect on the outcome of the election. Russia has repeatedly denied the allegations.
Trump was also asked about claims that he has made about the people illegally casting ballots in the election, with no evidence. The claim has been widely debunked.
"Well, many people have come out and said I am right, you know that," Trump said in the interview. O'Reilly replied "I know, but you have to have data to back that up."
"Let me just tell you — when you see illegals, people that are not citizens and they are on the registration rolls," Trump countered.
"Look Bill, we can be babies, but you take a look at the registration, you have illegals, you have dead people, you have this, it's really a bad situation, it's really bad."