Russia's President Vladimir Putin has discussed a future meeting with the US President-elect Donald Trump, but no exact date was appointed, the Kremlin said, rebutting media reports the two are already set for a tête-à-tête in January.

“It is true that during a [phone] conversation they talked about intentions to resume contacts, to arrange a meeting, but it has not been mentioned when this will happen,” Putin's press secretary Dmitry Peskov told reporters on Thursday.

Putin and Trump might meet after the latter's inauguration, but there is not even an estimated date, the Kremlin spokesman added, disconfirming media gossip on the matter. Peskov added that any official meeting before Trump is sworn-in had not been discussed at all.

Trump look forward to 'strong & enduring relationship w/ Russia' - statement after 1st phone conversation w/ Putin https://t.co/jchsNQkumP — RT (@RT_com) November 15, 2016

Trump, who was elected the 45th president of the United States on November 8, will formally be admitted to office on January 20. On Thursday, Russia's Izvestia newspaper reported, citing a high ranking source in the Republican Party, that the president-elect could have been planning to travel to Moscow even before that date. His advisers allegedly “managed to talk him out of the pre-inauguration visit,” the paper suggested, citing the anonymous source.

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Putin and Trump held their first telephone conversation after the US elections. They discussed ways to improve Russia-US relations and "constructive cooperation," as well as pressing international issues such as the Syrian crisis.

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The Russian president and the US president-elect agreed to keep in contact by telephone, the Kremlin later said, adding that the idea of a meeting in person had also been discussed.

In a message to Trump following his victory, Putin expressed confidence that "building a constructive dialogue between Moscow and Washington, based on principles of equality, mutual respect and each other's positions, meets the interests of the peoples of our countries and of the entire international community."

Trump's team also issued a statement, saying that the US president-elect is "very much looking forward to having a strong and enduring relationship with Russia and the people of Russia."