The statement comes after Trump on Sunday said he was "damn angry" with Putin in an interview with NBC News. It is said to have been based on Putin's statement about establishing a "temporary government" in Kyiv under UN supervision.
Trump added, however, that "the anger will dissipate quickly if he (Putin) does the right thing".
The President remains open to contact with President Trump, says the Kremlin's spokesperson Dmitrij Peskov to reporters in Moscow on Monday.
No conversation is planned at present, but it can, according to the Kremlin, be "organized quickly" if deemed necessary.
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