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President Donald Trump is drawing fire from Republicans and Democrats alike after playing down political assassinations in Russia and Moscow's invasion of Ukraine.

Trump -- now two weeks into his four-year term -- showed no signs of yielding to demands from within his own Republican Party to distance himself from President Vladimir Putin's regime, instead plunging himself into a fresh political firestorm.

"I do respect him. Well, I respect a lot of people, but that doesn't mean I'm going to get along with them," Trump said in an excerpt of an interview with Fox News's Bill O'Reilly that aired before the Super Bowl on Sunday.

When pressed in relation to Putin's alleged links to the extrajudicial killing of journalists and dissidents, Trump said, "we've got a lot of killers. You think our country's so innocent?"

"Take a look at what we've done too. We've made a lot of mistakes."

Trump's fellow Republicans, including Senate leader Mitch McConnell, were quick to criticize the president's remarks.

"I don't think there is any equivalency with the way the Russians conduct themselves and the way the United States does," McConnell said.

"He is a former KGB agent, a thug, not elected in a way that most people consider a credible election," he told CNN.

That criticism was echoed by Michael McFaul, a former ambassador to Russia and advisor to president Barack Obama, who described Trump's comments as "disgusting."

"This moral equivalency that Trumps continues to draw between the USA and Russia is disgusting (and inaccurate)," he said on Twitter.

'We're watching'

Trump's Vice President Mike Pence tried to explain the administration's approach to the conflict in eastern Ukraine, which had flared after Trump and Putin spoke by telephone a week ago.

"We're watching, and (we're) very troubled by the increased hostilities over the past week in eastern Ukraine," Pence told ABC's "This Week" news program.

The Kremlin said that during the Trump-Putin call the two men had discussed improving economic relations, a potential signal of Trump's willingness to lift sanctions on Russia.

Asked whether the administration would be willing to ease sanctions while Russia is violating ceasefire agreements, Pence demurred.

"I think that's a question that will be answered in the months ahead. And it just simply all depends," he said.

"If we have opportunities to work together, I think the president is looking for an opportunity to begin that relationship anew.

"But make no mistake about it -- those decisions will await action. And they'll be very dependent on how the Russians respond in the days ahead."