The US Embassy in Ukraine urged American citizens in Ukraine to consider departing now, saying that the security situation in the country was "unpredictable due to the increased threat of Russian military action."
The security situation in Ukraine "can deteriorate with little notice", the embassy said on its website on Wednesday.
Earlier this week the United States urged its citizens not to travel to Ukraine.
US President Joe Biden said on Tuesday that personal sanctions on Russian President Vladimir Putin, though a rare step, could be considered as part of a drive by Washington and its allies to convince Moscow that any new aggression against Ukraine would have swift and massive costs.
Russia warned on Wednesday that imposing sanctions on Putin personally would not hurt him but would be "politically destructive."
Russia has gathered tens of thousands of troops near its border with Ukraine but has denied that it plans to invade.
The United States has spent weeks trying to build agreement with European partners on a strong sanctions package if Russia attacks.