Megyn Kelly said the US President hurled abuse at other premiers but was “so nice” to Mr Putin over fears Moscow could publish damaging information about him.
Mr Putin dismissed the idea that the Mr Trump had singled him out for any preferential treatment, telling the NBC New host that, he merely showed a “partner respect”.
Kelly asked the Russian leader:“Anytime he says anything about you, it is extremely deferential, never a harsh word for you, although if you look at the way he speaks about members of his own party, of his own staff, never mind other political leaders, he frequently, personally insults them. Why do you think he’s so nice to you?”
Mr Putin replied via an interpreter: “I don’t believe he treats me personally with reverence. He understands that if you need to cooperate with someone you must treat your future or current partner with respect, otherwise nothing will come of it.”
In a separate interview about her conversation with the Russian President, Kelly told MSNBC presenter Chris Matthews: “I would not say that Putin likes Trump. I did not glean that at all from him. I did glean that perhaps he has something on Donald Trump.
She added: “I think there’s a very good chance Putin knows some things about Donald Trump that Mr. Trump does not want repeated publicly,” she added.
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Her comments came as the FBI continues to investigate possible collusion between Mr Trump’s election campaign and Russian hackers, who are alleged to have stolen information linked to the campaign of his rival Hillary Clinton and passed it to Wikileaks so it could be released to undermine her.
A dossier by former British spy Christopher Steele ahead of the election claimed that Mr Trump had deep ties with Russia, and also that he was involved in lewd acts in a five-star hotel during a 2013 trip to Moscow.
The memo was given to an FBI inquiry which is investigating alleged collusion between the Kremlin and Mr Trump’s election campaign.
The agency last month charged 13 Russian nationals and three internet companies in the country over claims they ran a social media campaign “supporting” Mr Trump’s White House bid.
Mr Putin said “so what” over the claims, saying in the NBC interview that even if those charged were found guilty they had no links to the Kremlin.
He even suggested minorities in Russia might have been to blame, saying: “Maybe they’re Ukrainians, Tatars, Jews, just with Russian citizenship. Even that needs to be checked.”