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3 year oldMr Biden, who spoke to Mr Floyd's family on Monday, said he believed the case was "overwhelming".
His comments came as the jury meets for a second day to consider its verdict.
Mr Chauvin, 45, was filmed kneeling on Mr Floyd's neck for more than nine minutes during his arrest last May.
He is on trial for charges including second-degree murder and has pleaded not guilty.
The footage of Mr Chauvin, who is white, with his knee on African-American Mr Floyd's neck sparked global protests against racism. Cities around the US are bracing for renewed protests regardless of the verdict.
White House spokeswoman Jen Psaki said the president spoke to Mr Floyd's family on Monday to "check in with them and also share that the family was in his prayers".
"The jury is sequestered... he certainly is not looking to influence [the trial]," she added.
Mr Biden spoke in more detail about the call at the White House on Tuesday. "I can only imagine the pressure and anxiety they are feeling," he said of the family.
"I waited until the jury was sequestered and I called [them]," he said. "They're calling for peace... no matter what that verdict is."
"I'm praying the verdict is the right verdict," Mr Biden added. "I think [the evidence] is overwhelming."
Earlier on Tuesday, Mr Floyd's younger brother confirmed that he had spoken to the president.
"[Mr Biden] knows how it is to lose a family member, and he knows the process of what we're going through," Philonise Floyd told NBC News. "He was just letting us know that he was praying for us."
Mr Biden lost his first wife, Neilia, and baby daughter, Naomi, in a car accident in 1972. In 2015, his son Beau died of brain cancer at the age of 46.
The jury has retired to consider testimony from 45 witnesses, including doctors, use-of-force experts, police officers, bystanders and people who were close to Mr Floyd.
Mr Chauvin is charged with second-degree unintentional murder, third-degree murder and manslaughter. He faces up to 40 years in prison if convicted of the most serious charge - second-degree murder.
A conviction on any of the counts against him will require the jury to return a unanimous verdict. A single juror holding out would result in a mistrial, but the state could then try Mr Chauvin again.
Of the 12 jurors, six are white, four are black and two are multiracial. Seven are women and five are men.
On Monday, the governor of Minnesota, Tim Walz, requested security assistance from the states of Ohio and Nebraska ahead of the verdict.
The prosecution and defence made their closing statements on Monday following a trial that lasted three weeks
Mr Chauvin's lawyer Eric Nelson argued that his client did what any "reasonable police officer" would have done after finding himself in a "dynamic" and "fluid" situation involving a large man scuffling with three officers.
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