There are reports of armed groups planning to gather at all 50 state capitols and in Washington DC in the run-up to his 20 January inauguration.
The fears come as security plans are hardened for the event itself.
On Monday, Mr Biden told reporters he was not afraid to take the oath of office outside of the US Capitol.
Both he and Vice-President-elect Kamala Harris are still expected to be sworn in outside the building, only two weeks after it was the site of a deadly raid by radical supporters of President Donald Trump opposing the election result.
Security officials are resolute there will be no repeat of the breach seen on 6 January – when thousands of pro-Trump supporters were able to break into the grounds of the complex where members of Congress were voting to certify the election result.
Chad Wolf, acting head of the Department of Homeland Security, said Monday that he had instructed the US Secret Service to begin special operations for the inauguration on Wednesday – six days early – “in light of events of the past week and the evolving security landscape”.
Officials say up to 15,000 National Guard troops could be made available to fortify the event.
Later on Monday, Mr Wolf became the third Trump cabinet secretary to step down since the Capitol riots, after Betsy DeVos and Elaine Chao.
Mr Wolf’s exit plunged his department into turmoil just as it gears up to handle security for the Biden inauguration. Mr Wolf last week called on Mr Trump to “strongly condemn” the protesters who stormed Congress.
The outgoing secretary said his departure had been prompted by “recent events”, including court rulings challenging the legal validity of his appointment.
Law enforcement around the country are said to be bracing for the possibility of further violence in the days before Joe Biden takes office.
Posts on pro-Trump and far-right online networks have called for protest action on a number of dates, including armed demonstrations in cities across the country on 17 January and a march in Washington DC on inauguration day itself.
An internal FBI bulletin, reported by ABC News and other outlets, carries a warning that one group is calling for the “storming” of state, local and federal courthouses around the country if Mr Trump is removed from office early and on inauguration day if he is not.
Calls for Mr Trump’s resignation, removal from office or impeachment have grown among Democrats and some Republicans in the days following the riots.
Local police agencies have been told by federal law enforcement to increase security at statehouses following last week’s violence, according to US media.
The Reuters news agency, citing a federal law enforcement official, said the FBI warnings are in place for all state capitals from 16 to 20 January itself and in Washington DC at least three days before the inauguration.
Although the violence at the US Capitol dominated headlines last week, similar smaller incidents were reported elsewhere in the country at the same time.
The US Department of Homeland Security confirmed on Monday that it would begin National Special Security Event (NSSE) operations for the inauguration six days early, starting Wednesday.
The designation allows a wide range of security and law enforcement agencies to coordinate together on special protective measures, like enforcing road closures and a secure perimeter.
The announcement came after Washington DC’s Mayor, Ms Bowser, went public with her appeal to bolster security after what she described as an “unprecedented terrorist attack” at the US Capitol last week.
She has also asked Americans to avoid travel to Washington DC for the event. Inaugurations traditionally draw hundreds of thousands to the streets of the capital, but the coronavirus pandemic had already curtailed those plans before security fears were heightened. (Courtesy BBC)