Tension has been rising between Russia and Western countries, who fear Russia plans to invade its neighbour Ukraine.
Russia denies this, but says Nato must rule out Ukraine and others ever joining Nato to defuse the situation.
Moscow wants urgent talks with the US - but its proposals are being viewed as a non-starter in Washington.
Responding to Moscow's call for direct negotiations with the US, White House spokeswoman Jen Psaki told reporters: "There will be no talks on European security without our European allies and partners."
Nato, which was originally set up to defend Europe against possible threats from the former Soviet Union, has forces in the Baltic republics and Poland.
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