In dramatic scenes, demonstrators swarmed near the building, as Congress members were escorted out by police.
A joint session of Congress has been counting and confirming electoral college votes.
The proceedings are usually brief and ceremonial but Republican lawmakers are objecting to some results.
Any attempts to block Mr Biden's victory are almost certain to fail.
For days Mr Trump has also been putting pressure on Vice-President Mike Pence, who is presiding over the session, to block certification of the result.