Russia sought an apology from Fox News on Monday after the program host Bill O’Reilly described President Vladimir V. Putin as “a killer” during an interview with President Trump.

The Kremlin’s spokesman, Dmitri S. Peskov, told reporters that the description was “unacceptable, insulting,” according to the state-run news agencies RIA Novosti and Interfax.

“We consider such words from a Fox News correspondent to be unacceptable, insulting,” he said. “Of course, we would prefer to receive apologies to our president from such a respectable television network.”

In the interview, which aired on Sunday, Mr. O’Reilly asked Mr. Trump how he felt about the Russian leader.

Mr. O’Reilly: “Do you respect Putin?”

Mr. Trump: “I do respect him.”

Mr. O’Reilly: “Do you? Why?”

Mr. Trump: “Well, I respect a lot of people, but that doesn’t mean I’m going to get along with them. 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 — major fight — that’s a good thing. Will I get along with him? I have no idea. It’s very possible that I won’t.”

Mr. O’Reilly: “He’s a killer though. Putin’s a killer.”

Mr. Trump: “There are a lot of killers. You think our country’s so innocent?”

The president’s response, which appeared to equate Mr. Putin’s actions with those of the United States, drew outrage and dismay on social media.

An open admirer of the Russian leader, Mr. Trump has taken a conciliatory approach toward Mr. Putin, whose tenure has been known for human rights abuses, the brutal suppression of political dissent and the unnatural deaths of many political opponents.

Mr. Peskov declined to comment on Mr. Trump’s response to Mr. O’Reilly.

Representatives of Fox News did not immediately respond on Monday to a request for comment.