An invasion could start with aerial bombing that would make departures difficult and endanger civilians, the White House said on Friday.
Moscow has repeatedly denied any plans to invade Ukraine despite massing more than 100,000 troops near the border.
A host of other countries have also urged their nationals to leave Ukraine.
They include the UK, Canada, the Netherlands, Latvia, Japan and South Korea.
Russia's foreign ministry has accused Western countries of spreading false information.
