Mr Biden called the event “an assault on the Citadel of Liberty” and called on President Trump to “step up”.
“The scenes of chaos of the Capitol, do not reflect a true America; do not represent who we are,” Mr Biden told the assembled press at the Queen’s Theatre in Delaware.
“What we're seeing are a small number of extremists dedicated to lawlessness.
“This is not dissent. This is disorder.”
Protesters over-ran police stationed outside the building during a joint session of Congress, where Vice President Mike Pence was acting in his ceremonial role as President of the Senate.
Senators and US Representatives had to be evacuated from the Senate chamber - and Mr Pence was taken by Secret Service agents to a secure location - part way through the process of certifying Mr Biden’s Electoral College victory.
The joint session, which has been held every four years since the United States was founded, is considered a political formality.
Mr Biden said: “I call on this mob to pull back and allow the work of democracy to go forward.
“The words of a president matter, no matter how good or bad that President is.
“At their best, the words of a president can inspire. At their worst, they can incite.”
He told Mr Trump to “step up”, adding that “the world is watching.”
“I call on President Trump to go on national television now to fulfil his oath and defend the Constitution and demand an end to this siege.”
Moments after Mr Biden finished speaking, President Trump addressed the protesters in a video posted on Twitter, insisting they “have to go home now”.
However, he repeated the unfounded claim that the election had been “stolen” from him and his supporters.
The Capitol building is now back under the control the law-enforcement officers, according to US Officials.