US National Security Adviser Jake Sullivan told his Russian equivalent on Monday that Washington is ready to engage in diplomacy through several channels, including bilateral engagement, the White House said.
Mr Sullivan told Yuriy Ushakov, foreign policy adviser to Russian President Vladimir Putin, that "any dialogue must be based on reciprocity and address our concerns about Russia's actions", Washington said.
Moscow, which has unnerved the West with a troop build-up near Ukraine, last week unveiled a wish list of security proposals it wants to negotiate, including a promise that Nato would give up any military activity in Eastern Europe and Ukraine.
Washington has said some of Russia's proposals are unacceptable, but that the US will respond at some time this week with more concrete proposals on the format of any talks.
Konstantin Gavrilov, a Russian diplomat in Vienna, said that relations between Moscow and Nato had reached a "moment of truth".
"The conversation needs to be serious and everyone in Nato understands perfectly well despite their strength and power that concrete political action needs to be taken, otherwise the alternative is a military-technical and military response from Russia," Mr Gavrilov told RIA news agency.
The US response is likely to affect Moscow's thinking over Ukraine, which has become the main flashpoint in East-West relations.
The US and Ukraine say Russia may be preparing an invasion of its former Soviet neighbour.
Russia denies that and says it is Ukraine's growing relationship with Nato that has caused the stand-off to intensify. It has compared it to the 1962 Cuban missile crisis, when the world came to the brink of nuclear war.
Meanwhile, the US State Department on Monday advised its citizens to not travel to Ukraine because of “increased threats” from Russia along the border.
The State Department regularly issues travel advisories and had one in place for Ukraine already because of Covid-19.
But this was unusual because of the direct warning about the massing of Russian troops along the border.
Agencies contributed to this report