American citizens in Ukraine are being urged to consider leaving because of the “increased threat of Russian military action”.
The US embassy in the country said the “situation continues to be unpredictable” and could “deteriorate with little notice”.
It added: “The US Embassy urges US citizens in Ukraine to consider departing now using commercial or other privately available transportation options.”
Earlier, the UK and US both said that personal sanctions could be imposed on Vladimir Putin if Russia invades its neighbour.
Asked on Sky News whether the Russian president may be targeted individually, Foreign Secretary Liz Truss said ministers are “not ruling anything out”.
She also said new legislation will be introduced to make Britain’s sanctions regime tougher “so we are able to target more companies and individuals in Russia”.
Ms Truss added: “We are urging Russia to desist from an incursion and we’re making it very clear that if they were to do that there would be severe economic cost to Russia – severe sanctions.”
Defensive weapons and economic support are being supplied to Ukraine, she said.
So far, most US sanctions have hit Mr Putin’s allies and Russian trade.
But President Biden, asked if he would consider sanctioning Mr Putin personally if there was an offensive, said: “Yes, I would see that.”
It would be a rare move as the US normally does not impose sanctions on the leaders of foreign countries.
Kremlin spokesman Dmitry Peskov said such a tactic would be politically destructive but not painful, adding that anyone making the suggestion does not have enough expert knowledge of the subject.
Russia condemns the West’s ‘aggressive course’
In a sign of the tension being generated, Russian Foreign Minister Sergey Lavrov said that “if the West continues its aggressive course, Moscow will take the necessary retaliatory measures”.
Russia is waiting for answers from Washington – after demanding that Ukraine and other former Soviet nations never become members of NATO.
On a more positive note, four-way talks being held in Paris are a “strong signal of readiness for a peaceful settlement”, said Andriy Yermak, chief of staff to Ukraine’s president, on Wednesday.
Russia, Germany and France and also involved.
Germany is supplying 5,000 military helmets to Ukraine, while Spanish Prime Minister Pedro Sanchez said Russia would face major economic consequences if military action against Ukraine went ahead.
Russia has held new military drills on both land and sea and moved more paratroopers and fighter jets to Belarus, north of Ukraine, for what it said were joint exercises there next month.
War would ‘change the world’ – Biden
Joe Biden said there would be “enormous consequences” for the world if President Putin’s forces pushed into the former Soviet state, which lies on its southwestern border.
American F-15 jets landed at an Estonian airbase on Wednesday, the Lithuanian Defence Ministry said, as part of a move by NATO to bolster its eastern flank.
Some 8,500 US troops have been put on heightened alert to go to eastern Europe to bolster NATO forces.
The soldiers are on standby and the US president said some could be deployed quickly if needed, while a Pentagon official said more could be added to the current figure.
However the president vowed no American troops would be sent specifically to Ukraine.
Mr Biden also said that if Russia invades Ukraine with all of its forces, it would be the “largest invasion since World War Two” and would “change the world”.
Meanwhile, Boris Johnson has said Britain is prepared to send troops to protect NATO allies in Europe if there is an invasion and warned Mr Putin his forces would face “ferocious” Ukrainian resistance.
The prime minister also expressed concerns that a major military assault would lead to “bloodshed comparable to the first war in Chechnya or Bosnia”.
And in a televised address on Tuesday evening, Ukrainian President Volodymyr Zelenskiy urged his citizens to stay calm and said work was taking place for a meeting between him and the leaders of Russia, Germany and France.
Tensions remain high after NATO said on Monday it was putting forces on standby and sending more ships and fighter jets to eastern Europe in response to Russia’s troop build-up near the Ukraine border.
NATO currently has about 4,000 troops in multinational battalions in Estonia, Lithuania, Latvia and Poland, backed by tanks, air defences and intelligence and surveillance units.
Russia watching with ‘great concern’
Moscow has denied it is planning an assault and said it was watching with “great concern”.
It has massed about 100,000 troops near Ukraine in recent weeks and is holding military drills at multiple locations in Russia and neighbouring Belarus, which also borders Ukraine.
This has led the US and its NATO allies to rush to prepare for a possible war.
Russia is demanding security guarantees from the West, including that NATO must rule out allowing Ukraine to join the pact as it views the former Soviet republic as a buffer between itself and NATO countries.