Russian President Vladimir Putin is calling on Fox News to apologise after talk show host Bill O'Reilly called him a "killer" during a Sunday interview with US President Donald Trump.

"We believe these words by a Fox News correspondent unacceptable, offensive and we would prefer to receive an apology to the president of Russia from such a respected broadcaster," said the Russian president's press secretary Dmitry Peskov early Monday.

President Trump appeared in an interview with O'Reilly that was aired just before the American Super Bowl.

Trump has repeatedly expressed his admiration for Putin. When questioned by O'Reilly about why he respects him, Trump said "I respect a lot of people but that doesn't mean I'm going to get along with him." Having Russia on America's side is key to fighting "Islamic terrorism all over the world," Trump said.

"But he's a killer though. Putin's a killer," O'Reilly shot back. A long list of critics of President Putin have turned up dead or been assassinated in contract killings, but the president has never been directly connected to any of these.

On his death bed in 2006, however, Alexander Litvinenko, who was poisoned with radioactive polonium by assassins in London, accused Putin of sanctioning his murder. In 2014, Russia violently invaded and annexed sections of eastern Ukraine, and in Syria Russia has indiscriminately bombed civilians in support of the autocrat Bashar al-Assad.

Trump appeared to defend Putin against O'Reilly during the interview, saying "there are a lot of killers" in the United States. "We've got a lot of killers. What do you think — our country's so innocent. You think our country's so innocent?" Trump said.