The Russian leader, a former KGB intelligence officer, is not given to unguarded moments or admissions of guilt. When Kelly asked him about allegations of Russian involvement in the campaign, he replied with a conspiracy theory about the death of President John F. Kennedy in 1963.
"There's a theory that Kennedy's assassination was arranged by the United States intelligence services. So, if this theory is correct - and that can't be ruled out - " then the same agencies could fabricate evidence of Russian hacking, Putin said.
In several cases, Putin said he was not even aware of contacts reported in American media. For instance, Kelly asked about an episode first reported in the Washington Post, in which Jared Kushner - the President's son-in-law and senior adviser - suggested setting up a secret back-channel communication with the Kremlin before Trump took office.
"I don't know about this proposal. No proposal like that came to me," Putin said, speaking via a Russian interpreter. Putin said such a request would have been reported to him. "For me, this is just amazing. You created a sensation out of nothing, and . . . you turned it into a weapon of war against the current president."
Putin also rejected the idea that he had any relationship with Michael Flynn, Trump's former national security adviser. In 2015, Flynn visited Moscow for a banquet honouring Russian TV outlet RT, and photos show him seated next to Putin.
Putin said that he had not sat in the seat for much of the dinner, and that he barely spoke to Flynn. "I didn't even really talk to him. That's the extent of my acquaintance with Mr Flynn," he said.
Kelly asked Putin if he was holding any kind of damaging information about Trump, either involving Trump's finances or a visit Trump made to Russia as a businessman. Putin, slouched over in his seat, scoffed at the idea.
"We have a lot of Americans who visit us," Putin said. "Do you think we're gathering compromising information on all of them right now or something? Are you all - have you all lost your senses over there?"
Intelligence experts have said Russian intelligence officials have a habit of trying to gather compromising information on influential foreigners when they visit.
Among the denials, however, were signs of Putin's resentment toward the United States and its conduct as the world's lone post-cold war superpower.
Putin, for instance, dismissed Kelly's questions about repression and the killing of journalists in Russia by saying it was another example of American moralising. "Why do you feel you have the right to ask us these kinds of questions?" he said.
At another point, Putin answered Kelly's questions about Russia's role in the election by saying that the United States had sought to influence other nations' elections in the past. "Put your finger anywhere on a map of the world," he said, "and everywhere you will hear complaints that American officials are interfering in internal election processes."
Among Putin's denials that the Russians had interfered in the US election, he had just offered up a moral logic for Russia - interfering in US elections.
"That sounds like a justification," Kelly said.
"It doesn't sound like a justification," Putin said. "It sounds like a statement of fact. Every action has an equal and opposite reaction."
