WASHINGTON—President Donald Trump appeared to draw an equivalence between Russian President Vladimir Putin and the behavior of the U.S. when he responded to a remark about Mr. Putin being a “killer” by saying: “We got a lot of killers—what, you think our country’s so innocent?”

The statement, made in an interview with Fox News host Bill O’Reilly that will air before Sunday’s Super Bowl, came after Mr. Trump again said he respected the Russian president and Russia could help in the fight against Islamic State and other terrorists....