The move came as the US announced plans to evacuate its embassy in the Ukrainian capital Kyiv.
Before talking to Mr Biden on Saturday, the Russian leader will share a call with French president Emmanuel Macron, who met with him in Moscow earlier in the week in a bid to resolve the crisis.
Russia has massed troops near the Ukraine border and has sent personnel to military exercises in neighbouring Belarus, but insistently denies that it intends to launch an offensive against Ukraine.
Adding to the sense of crisis, the Pentagon has ordered an additional 3,000 US troops to Poland to reassure allies.
Mr Biden has said the US military will not enter a war in Ukraine, but he has promised severe economic sanctions against Moscow, in concert with international allies.
The timing of any possible Russian military action remains a key question.
The US picked up intelligence that Russia is looking at Wednesday as a target date, according to a US official.
The official would not say how definitive the intelligence was, and the White House publicly underlined that the US does not know with certainty whether Mr Putin is committed to invasion.
However, American officials said that Russia's build-up of offensive air, land and sea firepower near Ukraine has reached the point where it could invade on short notice.
US officials told The Associated Press that the US state department plans to announce on Saturday that virtually all American staff at the Kyiv embassy will be required to leave, although the state department would not comment.
The department had earlier ordered families of US embassy staffers in Kyiv to leave. But it had left it to the discretion of non-essential personnel if they wanted to depart.
Mr Biden's national security adviser, Jake Sullivan, urged all Americans in Ukraine to leave, emphasising that they should not expect the US military to rescue them in the event that air and rail transportation is severed after a Russian invasion.
Several Nato allies including the UK, Canada, Norway and Denmark also are asking their citizens to leave Ukraine, as is non-Nato ally New Zealand.
Mr Sullivan said Russian military action could start with missile and air attacks, followed by a ground offensive.
"Yes, it is an urgent message because we are in an urgent situation," he told reporters at the White House.
"Russia has all the forces it needs to conduct a major military action," Mr Sullivan said, adding, "Russia could choose, in very short order, to commence a major military action against Ukraine."
He said the scale of such an invasion could range from a limited incursion to a strike on Kyiv, the capital.
Russian officials scoffed at the American claims. Foreign ministry spokeswoman Maria Zakharova said: "The hysteria of the White House is more indicative than ever.
"The Anglo-Saxons need a war. At any cost. Provocations, misinformation and threats are a favourite method of solving their own problems."
In addition to the more than 100,000 ground troops that US officials say Russia has assembled along Ukraine's eastern and southern borders, the Russians have deployed missile, air, naval and special operations forces, as well as supplies to sustain a war.
This week, Russia moved six amphibious assault ships into the Black Sea, augmenting its capability to land marines on the coast.
Mr Sullivan's stark warning accelerated the projected timeframe for a potential invasion, which many analysts had believed was unlikely until after the Winter Olympics in China end on February 20.
He said the combination of a further Russian troop build-up on Ukraine's borders and unspecified intelligence indicators have prompted the administration to warn that war could begin at any time.
"We can't pinpoint the day at this point, and we can't pinpoint the hour, but that is a very, very distinct possibility," Mr Sullivan said.
Mr Biden has said US troops will not enter Ukraine to contest any Russian invasion, but he has bolstered the American military presence in Europe as reassurance to allies on Nato's eastern flank.
On Friday the Pentagon said Mr Biden ordered a further 3,000 soldiers to Poland, on top of 1,700 who are on their way there. The US army is also shifting 1,000 soldiers from Germany to Romania, which like Poland shares a border with Ukraine.
Mr Biden spoke to a number of European leaders on Friday to underscore the concerns raised by US intelligence about the potential imminence of a Russian invasion.
Mr Sullivan said the Western leaders were completely united and would respond harshly to a Russian invasion with devastating economic and trade sanctions.
Russia is demanding that the West keeps Ukraine and other former Soviet countries out of Nato.
It also wants Nato to refrain from deploying weapons near its border and to roll back alliance forces from Eastern Europe - demands flatly rejected by the West.
Russia and Ukraine have been locked in a bitter conflict since 2014, when Ukraine's Kremlin-friendly leader was driven from office by a popular uprising.
Moscow responded by annexing Crimea and then backing a separatist insurgency in eastern Ukraine, where fighting has killed more than 14,000 people.
A 2015 peace deal brokered by France and Germany helped halt large-scale battles, but regular skirmishes have continued, and efforts to reach a political settlement have stalled.