He told a news conference Mr Putin would pay a “serious and dear price” for invading, but indicated a minor incursion might be treated differently.
The White House later stressed any Russian military move would be met with a swift, severe response from the West.
The Kremlin warned the comments could further destabilise the situation.
Russia has some 100,000 troops near the border but denies planning an invasion.
President Putin has made a series of demands to the West, insisting Ukraine should never be allowed to join Nato and that the defensive alliance abandons military activity in Eastern Europe.
“We have made it clear that any further eastward expansion of Nato is unacceptable,” Mr Putin said at a televised press conference last month.
Mr Putin’s exact reasons for the build up of Russian troops near Ukraine’s border are unknown, but many believe it is an attempt to force the West to take Russia’s security demands seriously.
On Thursday, US Secretary of State Antony Blinken is meeting foreign ministers from Germany, France and the UK to co-ordinate Western strategy over a potential invasion of Ukraine. He has previously warned that Russia could attack Ukraine at short notice.
At his news conference on Wednesday, Mr Biden said: “There are differences in Nato as to what countries are willing to do, depending on what happens.
“If there’s Russian forces crossing the border… I think that changes everything.
“What you’re going to see is that Russia will be held accountable if it invades and it depends on what it does,” he said. “It’s one thing if it’s a minor incursion, and then we end up having to fight about what to do and not do etc.”
White House officials rushed to clarify the US position after Mr Biden’s comments. “If any Russian military forces move across the Ukrainian border, that’s a renewed invasion, and it will be met with a swift, severe, and united response from the United States and our Allies,” Press Secretary Jen Psaki said.
In response, the Kremlin said that any warnings of disastrous consequences for Russia would not help to reduce tensions, and could even destabilise the situation further.
Russia says the West and Ukraine are creating an information campaign to cover for their own aggressive actions. A foreign ministry spokesperson, Maria Zakharova, warned that it could have “the most tragic consequences for regional and global security”.