The US has asked that the United Nations Security Council meet publicly on Monday to discuss Russia's "threatening behavior" against Ukraine.
Russia has massed around 100,000 troops near the border with Ukraine while denying it plans to invade.
Several rounds of talks have taken place without a breakthrough but both the US-led NATO military alliance and Russia have kept the door open to further dialogue.
"Russia is engaging in other destabilizing acts aimed at Ukraine, posing a clear threat to international peace and security and the UN Charter," ambassador Linda Thomas-Greenfield said in a statement.
"This is not a moment to wait and see. The council's full attention is needed now, and we look forward to direct and purposeful discussion on Monday," she said.
Meanwhile, Russia said that the US was failing to address its main security concerns over Ukraine but left the door open to further talks to ease tensions.
Amid continued fears that Russia could invade its pro-Western neighbour, Washington and Berlin also warned they could target the controversial Nord Stream 2 pipeline, which is set to double supplies of cheap natural gas from Russia to Germany.
Relations between Russia and the West have reached their lowest point since the Cold War after Moscow deployed tens of thousands of troops on the border of Ukraine.
Russia denies any plans to invade but last month demanded wide-ranging security guarantees from the West, including that Ukraine never be allowed to join the US-led NATO military alliance.
The US yesterday delivered a reply in co-ordination with NATO allies, rejecting a ban on Ukraine joining, but offering a new "diplomatic path" out of the crisis.
In its first reaction to the reply, the Kremlin was unimpressed but cautious.
"It cannot be said that our views were taken into account," President Vladimir Putin's spokesman Dmitry Peskov told reporters.
"Let's not rush into assessments, it takes time to analyse," he said, adding that the documents were with Mr Putin.
Moscow's chief concern ignored - Lavrov
Russian Foreign Minister Sergei Lavrov said Moscow's chief concern - the potential for Ukraine to join NATO - had been ignored, but that it would be possible to move forward on other issues.
"There is a response which gives hope for the start of a serious conversation on secondary questions," Mr Lavrov said.
US Secretary of State Antony Blinken said yesterday he would speak to Mr Lavrov again in the coming days and that the US response "sets out a serious diplomatic path forward should Russia choose it".
He renewed an offer of "reciprocal" measures including reductions of missiles in Europe and transparency on military drills and Western aid to Ukraine.
But he made clear that the US would not budge on Russia's core demand that Ukraine never be allowed to join NATO.
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'Ukraine in the middle'
The US has warned of severe and swift consequences if Russia invades, including possible personal sanctions on Putin.
US State Department spokesman Ned Price told National Public Radio (NPR) that despite concerns over gas supplies to Europe, the Nord Stream 2 pipeline was a possible target.
"If Russia invades Ukraine, one way or another, Nord Stream 2 will not move forward, and we want to be very clear about that," he said.
The pipeline was completed in September but has not yet been approved by Germany for use.
Initially wary of linking Nord Stream 2 to the Ukraine crisis, Germany has increasingly warned of potential consequences for the pipeline.
"We are working on a strong package of sanctions" with Western allies, and it covers several aspects "including Nord Stream 2", Foreign Minister Annalena Baerbock told parliament.
On the streets of Kyiv, there were concerns that Ukraine had been forgotten amid the high-level talks between Moscow, NATO and Washington.
"The United States is provoking Russia and Russia is provoking the United States. And somewhere in the middle is Ukraine," said Dmytro Sylenko, a 23-year-old businessman.
"Honestly, I don't care who is provoking whom, what matters to me is that there is peace. I don't care about the rest," he told AFP.
Russia, which has a fraught historical relationship with Ukraine, has fuelled an insurgency in the former Soviet republic's east that has killed more than 13,000 people since 2014.
That year Russia also seized Crimea after the overthrow of a pro-Russian government in Kyiv.
Talks in two weeks
The current crisis has seen NATO put 8,500 troops on standby, with the alliance's Secretary General Jens Stoltenberg saying yesterday that while it was working towards de-escalation, "we are also prepared for the worst".
In another bid to defuse tensions, senior Russian and Ukrainian officials met for eight hours in Paris with representatives of France and Germany yesterday.
Dmitry Kozak, the Kremlin deputy chief of staff, said the talks were "not simple" but that another round would take place in two weeks in Germany.
France said after the so-called Normandy Format talks that the envoys committed to a fragile July 2020 ceasefire in eastern Ukraine between government forces and pro-Moscow separatists.
Ukrainian President Volodymyr Zelensky "positively assesses the fact of the meeting, its constructive nature, as well as the intention to continue meaningful negotiations in two weeks in Berlin," his press service said in a statement.