An invasion could start with aerial bombing that would make departures difficult and endanger civilians, the White House said on Friday.
A host of other countries have also urged their nationals to leave Ukraine.
Moscow has repeatedly denied any plans to invade Ukraine despite massing more than 100,000 troops near the border.
Russia's foreign ministry on Friday accused Western countries of spreading false information.
US National Security Adviser Jake Sullivan said Russian forces were now "in a position to be able to mount a major military action" in remarks seen as a clear escalation in the urgency of warnings from US officials.
"We obviously cannot predict the future, we don't know exactly what is going to happen, but the risk is now high enough and the threat is now immediate enough that [leaving] is prudent," he said.
Mr Sullivan added that the administration did not know if Russian President Vladimir Putin had made a final decision to invade, but said that the Kremlin was looking for a pretext to justify military action, which he said could start with intense aerial bombardment.
His comments came as US officials warned of a further build-up of Russian troops at Ukraine's borders over the past week and planned Russian military exercises in the Black Sea in the coming days.
Earlier, US Secretary of State Antony Blinken said the increase in Russian forces at the border was "very troubling signs of Russian escalation".
"We're in a window when an invasion could begin at any time, and to be clear, that includes during the Olympics [which end on 20 February]," Mr Blinken said.
President Biden has said that he would not send troops to rescue any citizens left stranded in the event of Russian action.
On Friday, the US president hosted a video call with transatlantic leaders in which they agreed on co-ordinated action to inflict severe economic consequences on Russia if it invaded Ukraine.
The US also said it was deploying a further 3,000 troops from Fort Bragg, North Carolina, to Poland, and that they were expected to arrive there next week. The troops will not fight in Ukraine, but will ensure the defence of US allies.
Photo file Caption: US National Security Adviser Jake Sullivan