President Donald Trump has long expressed a desire for improved relations with Moscow, but his latest comments about Russian President Vladimir Putin and the US are leading some fellow Republicans to take a step back from the president — on this issue at least.

West Palm Beach, Florida: President Donald Trump has long expressed a desire for improved relations with Moscow, but his latest comments about Russian President Vladimir Putin and the US are leading some fellow Republicans to take a step back from the president — on this issue at least.

Told by Fox News' Bill O'Reilly during an interview that the Russian leader is "a killer," Trump said the US has killers, too.

"What do you think? Our country's so innocent?" Trump said during the taped interview broadcast during Sunday's Super Bowl pregame show.

Trump has praised Putin and signaled that US-Russia relations could be in for a makeover under his leadership, even after US intelligence agencies concluded that Russia meddled in the 2016 US presidential campaign to help Trump defeat Democrat Hillary Clinton.

During Putin's years in power, a number of prominent Russian opposition figures and journalists have been killed.

Trump says in the interview that he respects a lot of people, including Putin "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," Trump said, using an acronym for the Islamic State group. "Will I get along with him? I have no idea."

O'Reilly then said about Putin: "But he's a killer, though. 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?"

When O'Reilly says he doesn't know any US government leaders who are killers, Trump said "take a look at what we've done, too. We've made a lot of mistakes" and then he referenced the Iraq war.

The Kremlin voiced anger over O'Reilly's characterisation.

Dmitry Peskov, a spokesman for President Vladimir Putin, refused to comment on Trump's reply but lashed out at Fox, calling O'Reilly's remarks "unacceptable and offensive."

"We would like to receive an apology to the president from this respected organisation," Peskov told reporters on Monday, referring to Fox News.

At home, Republicans and Democrats took exception to Trump's comparison of Russia and the US.

"Putin's a former KGB agent. He's a thug. He was not elected in a way that most people would consider a credible election," Senate Majority Leader Mitch McConnell, R-Ky., told CNN's "State of the Union. "The Russians annexed Crimea, invaded Ukraine and messed around in our elections. And no, I don't think there's any equivalency between the way the Russians conduct themselves and the way the United States does."

Added Sen. Ben Sasse, of Nebraska, one of Trump's Republican critics: "There is no moral equivalency between the United States of America, the greatest freedom living nation in the history of the world, and the murderous thugs that are in Putin's defense of his cronyism."

O'Reilly also asked Trump to back up his claim that some 3 million to 5 million illegal votes were cast in the election. Trump didn't answer directly, but shifted to assert that immigrants in the US illegally and dead people are on the voter rolls.

"It's really a bad situation, it's really bad," Trump said.

There is no evidence of widespread voter fraud in the 8 November election. Trump won the Electoral College vote but lost the popular vote by nearly 2.9 million votes to Clinton.

Trump recently announced on Twitter that he would call for a "major investigation" into voter fraud. He said during the Fox News interview that he will set up a commission to be headed by Vice-President Mike Pence and "we're going to look at it very, very carefully."

Asked earlier about Trump's promised investigation, McConnell said he saw no federal role because states historically have handled voter fraud investigations. "I don't think we ought to spend any federal money investigating that," he said on CNN.

On other issues, Trump said in the interview that:

— California's consideration of legislation to become a statewide sanctuary for people living in the country illegally is "ridiculous." He suggested withholding federal funding as a possible punishment.

— Plans to enact a complete replacement for the Affordable Care Act could slip into next year. "I would like to say by the end of the year, at least the rudiments, but we should have something within the year and the following year."

— Living in the White House is "a surreal experience in a certain way, but you have to get over it, because there's so much work to be done."